diff --git a/applications/test/complex/Make/files b/applications/test/complex/Make/files
new file mode 100644
index 0000000000..9b48d7cbaf
--- /dev/null
+++ b/applications/test/complex/Make/files
@@ -0,0 +1,3 @@
+Test-complex.C
+
+EXE = $(FOAM_USER_APPBIN)/Test-complex
diff --git a/applications/test/complex/Make/options b/applications/test/complex/Make/options
new file mode 100644
index 0000000000..18e6fe47af
--- /dev/null
+++ b/applications/test/complex/Make/options
@@ -0,0 +1,2 @@
+/* EXE_INC = */
+/* EXE_LIBS = */
diff --git a/applications/test/complex/Test-complex.C b/applications/test/complex/Test-complex.C
new file mode 100644
index 0000000000..0cf31f9c85
--- /dev/null
+++ b/applications/test/complex/Test-complex.C
@@ -0,0 +1,93 @@
+/*---------------------------------------------------------------------------*\
+  =========                 |
+  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
+   \\    /   O peration     |
+    \\  /    A nd           | Copyright (C) 2019 OpenCFD Ltd.
+     \\/     M anipulation  |
+-------------------------------------------------------------------------------
+License
+    This file is part of OpenFOAM.
+
+    OpenFOAM is free software: you can redistribute it and/or modify it
+    under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+    for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with OpenFOAM.  If not, see <http://www.gnu.org/licenses/>.
+
+Application
+
+Description
+    Some tests for complex numbers
+\*---------------------------------------------------------------------------*/
+
+#include "argList.H"
+#include "complex.H"
+#include "complexVector.H"
+#include "Field.H"
+
+using namespace Foam;
+
+void print1(const complex& z)
+{
+    Info<<"r: " << z.real() << " i: " << z.imag() << nl;
+}
+
+
+// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
+//  Main program:
+
+int main(int argc, char *argv[])
+{
+    Info<< "complex()     : " << complex() << nl
+        << "complex(zero) : " << complex(Zero) << nl
+        << "complex::zero : " << complex::zero << nl
+        << "complex::one  : " << complex::one << nl
+        << "complex(scalar) : " << complex(3.14519) << nl
+        << nl;
+
+    Info<< "complexVector::zero : " << complexVector::zero << nl
+        << "complexVector::one  : " << complexVector::one << nl
+        << nl;
+
+    // Comparison
+
+    for (complex c :  { complex{1, 0}, complex{1, 2}} )
+    {
+        print1(c);
+        // TDB: allow implicit construct from scalar?
+        //
+        // if (c == 1.0)
+        // {
+        //     Info<< c << " == " << 1 << nl;
+        // }
+    }
+
+    Field<complex> fld1(3, complex(2.0, 1.0));
+
+    Info<< "Field " << flatOutput(fld1) << nl;
+
+    Info<< "sum = " << sum(fld1) << nl;
+    // Not yet Info<< "min = " << min(fld1) << nl;
+
+    fld1 *= 10;
+    Info<< "Multiply: " << flatOutput(fld1) << nl;
+
+    for (complex& c : fld1)
+    {
+        c = ~c;
+    }
+
+    Info<< "Conjugate: " << flatOutput(fld1) << nl;
+
+    Info<< "\nEnd\n" << endl;
+    return 0;
+}
+
+// ************************************************************************* //
diff --git a/src/OpenFOAM/primitives/Vector/complexVector/complexVector.C b/src/OpenFOAM/primitives/Vector/complexVector/complexVector.C
index 1b43be5cc5..bb99cf534b 100644
--- a/src/OpenFOAM/primitives/Vector/complexVector/complexVector.C
+++ b/src/OpenFOAM/primitives/Vector/complexVector/complexVector.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           |
+    \\  /    A nd           | Copyright (C) 2019 OpenCFD Ltd.
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
                             | Copyright (C) 2011-2016 OpenFOAM Foundation
@@ -44,13 +44,13 @@ const char* const Foam::complexVector::vsType::componentNames[] =
 template<>
 const Foam::complexVector Foam::complexVector::vsType::zero
 (
-    complexVector::uniform(complex(0, 0))
+    complexVector::uniform(complex::zero)
 );
 
 template<>
 const Foam::complexVector Foam::complexVector::vsType::one
 (
-    complexVector::uniform(complex(1, 1))
+    complexVector::uniform(complex::one)
 );
 
 template<>
diff --git a/src/OpenFOAM/primitives/complex/complex.C b/src/OpenFOAM/primitives/complex/complex.C
index 89aa30c14f..a85f596fdc 100644
--- a/src/OpenFOAM/primitives/complex/complex.C
+++ b/src/OpenFOAM/primitives/complex/complex.C
@@ -2,7 +2,7 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           |
+    \\  /    A nd           | Copyright (C) 2019 OpenCFD Ltd.
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
                             | Copyright (C) 2011 OpenFOAM Foundation
@@ -28,14 +28,13 @@ License
 #include "complex.H"
 #include "IOstreams.H"
 
-#include <sstream>
-
 // * * * * * * * * * * * * * * Static Data Members * * * * * * * * * * * * * //
 
 const char* const Foam::complex::typeName = "complex";
 const Foam::complex Foam::complex::zero(0, 0);
 const Foam::complex Foam::complex::one(1, 1);
 
+
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
 Foam::complex::complex(Istream& is)
@@ -48,9 +47,7 @@ Foam::complex::complex(Istream& is)
 
 Foam::word Foam::name(const complex& c)
 {
-    std::ostringstream buf;
-    buf << '(' << c.Re() << ',' << c.Im() << ')';
-    return buf.str();
+    return '(' + std::to_string(c.Re()) + ',' + std::to_string(c.Im()) + ')';
 }
 
 
@@ -58,12 +55,10 @@ Foam::word Foam::name(const complex& c)
 
 Foam::Istream& Foam::operator>>(Istream& is, complex& c)
 {
-    // Read beginning of complex
     is.readBegin("complex");
 
     is  >> c.re >> c.im;
 
-    // Read end of complex
     is.readEnd("complex");
 
     is.check(FUNCTION_NAME);
diff --git a/src/OpenFOAM/primitives/complex/complex.H b/src/OpenFOAM/primitives/complex/complex.H
index 0ffe362ed6..c4b258a06e 100644
--- a/src/OpenFOAM/primitives/complex/complex.H
+++ b/src/OpenFOAM/primitives/complex/complex.H
@@ -2,10 +2,10 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           |
+    \\  /    A nd           | Copyright (C) 2019 OpenCFD Ltd.
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-                            | Copyright (C) 2011-2016 OpenFOAM Foundation
+                            | Copyright (C) 2011-2014 OpenFOAM Foundation
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -27,7 +27,7 @@ Class
     Foam::complex
 
 Description
-    Extension to the c++ complex library type.
+    A complex number, similar to the C++ complex type.
 
 SourceFiles
     complexI.H
@@ -39,8 +39,8 @@ SourceFiles
 #define complex_H
 
 #include "scalar.H"
-#include "bool.H"
 #include "word.H"
+#include "zero.H"
 #include "contiguous.H"
 
 // * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
@@ -48,15 +48,14 @@ SourceFiles
 namespace Foam
 {
 
-// Forward declaration of friend functions and operators
-
+// Forward Declarations
 class complex;
 
 inline scalar magSqr(const complex&);
-inline complex sqr(const complex&);
 inline scalar mag(const complex&);
-inline const complex& max(const complex&, const complex&);
+inline complex sqr(const complex&);
 inline const complex& min(const complex&, const complex&);
+inline const complex& max(const complex&, const complex&);
 inline complex limit(const complex&, const complex&);
 inline const complex& sum(const complex&);
 inline complex operator+(const complex&, const complex&);
@@ -68,8 +67,9 @@ inline complex operator*(const scalar, const complex&);
 inline complex operator*(const complex&, const scalar);
 inline complex operator/(const complex&, const scalar);
 inline complex operator/(const scalar, const complex&);
-Istream& operator>>(Istream&, complex&);
-Ostream& operator<<(Ostream&, const complex&);
+
+Istream& operator>>(Istream& is, complex& c);
+Ostream& operator<<(Ostream& os, const complex& c);
 
 
 /*---------------------------------------------------------------------------*\
@@ -78,114 +78,166 @@ Ostream& operator<<(Ostream&, const complex&);
 
 class complex
 {
-    // private data
+    // Private Data
 
-        //- Real and imaginary parts of the complex number
+        //- Real and imaginary parts
         scalar re, im;
 
+
 public:
 
     //- Component type
     typedef complex cmptType;
 
 
-    // Static data members
+    // Static Data Members
 
+        //- The type name is "complex"
         static const char* const typeName;
 
+        //- A complex zero (0,0)
         static const complex zero;
+
+        //- A complex one (1,1)
         static const complex one;
 
 
     // Constructors
 
-        //- Construct null
-        inline complex();
+        //- Construct null as zero-initialized
+        inline constexpr complex() noexcept;
 
-        //- Construct given real and imaginary parts
-        inline complex(const scalar Re, const scalar Im);
+        //- Default copy constructor
+        complex(const complex&) = default;
+
+        //- Construct zero-initialized from zero class
+        inline constexpr complex(const Foam::zero) noexcept;
+
+        //- Construct from real component
+        inline explicit constexpr complex(const scalar r) noexcept;
+
+        //- Construct from real and imaginary parts
+        inline constexpr complex(const scalar r, const scalar i) noexcept;
 
         //- Construct from Istream
-        complex(Istream&);
+        explicit complex(Istream& is);
 
 
-    // Member functions
+    // Member Functions
 
-           // Access
+    // STL getter/setter
 
-               inline scalar Re() const;
-               inline scalar Im() const;
+        //- Real part of complex number - STL naming
+        constexpr scalar real() const
+        {
+            return re;
+        }
 
-           // Edit
+        //- Imaginary part of complex number - STL naming
+        constexpr scalar imag() const
+        {
+            return im;
+        }
 
-               inline scalar& Re();
-               inline scalar& Im();
+        //- Set real part of complex number - STL naming
+        inline void real(scalar val);
 
-           // Operators
-
-               inline complex conjugate() const;
+        //- Set imaginary part of complex number - STL naming
+        inline void imag(scalar val);
 
 
-    // Member operators
+    // Access
 
-        inline void operator=(const complex&);
-        inline void operator+=(const complex&);
-        inline void operator-=(const complex&);
-        inline void operator*=(const complex&);
-        inline void operator/=(const complex&);
+        //- Real part of complex number
+        inline scalar Re() const;
 
-        inline void operator=(const scalar);
-        inline void operator+=(const scalar);
-        inline void operator-=(const scalar);
-        inline void operator*=(const scalar);
-        inline void operator/=(const scalar);
+        //- Imaginary part of complex number
+        inline scalar Im() const;
 
+
+    // Edit
+
+        //- Real part of complex number
+        inline scalar& Re();
+
+        //- Imaginary part of complex number
+        inline scalar& Im();
+
+
+    // Operations
+
+        //- Complex conjugate
+        inline complex conjugate() const;
+
+
+    // Member Operators
+
+        //- Copy assignment
+        inline void operator=(const complex& c);
+
+        //- Assign zero
+        inline void operator=(const Foam::zero);
+
+        inline void operator+=(const complex& c);
+        inline void operator-=(const complex& c);
+        inline void operator*=(const complex& c);
+        inline void operator/=(const complex& c);
+
+        inline void operator=(const scalar s);
+        inline void operator+=(const scalar s);
+        inline void operator-=(const scalar s);
+        inline void operator*=(const scalar s);
+        inline void operator/=(const scalar s);
+
+        //- Conjugate
+        inline complex operator~() const;
+
+        //- Conjugate
         inline complex operator!() const;
 
-        inline bool operator==(const complex&) const;
-        inline bool operator!=(const complex&) const;
+        inline bool operator==(const complex& c) const;
+        inline bool operator!=(const complex& c) const;
 
 
-    // Friend functions
+    // Friend Functions
 
         friend scalar magSqr(const complex& c);
-        friend complex sqr(const complex& c);
         friend scalar mag(const complex& c);
-        friend const complex& max(const complex&, const complex&);
+        friend complex sqr(const complex& c);
         friend const complex& min(const complex&, const complex&);
+        friend const complex& max(const complex&, const complex&);
 
         friend complex limit(const complex&, const complex&);
 
         friend const complex& sum(const complex&);
 
 
-    // Friend operators
+    // Friend Operators
 
-        friend complex operator+(const complex&, const complex&);
-        friend complex operator-(const complex&);
-        friend complex operator-(const complex&, const complex&);
-        friend complex operator*(const complex&, const complex&);
-        friend complex operator/(const complex&, const complex&);
+        friend complex operator+(const complex& c1, const complex& c2);
+        friend complex operator-(const complex& c);
+        friend complex operator-(const complex& c1, const complex& c2);
+        friend complex operator*(const complex& c1, const complex& c2);
+        friend complex operator/(const complex& c1, const complex& c2);
 
-        friend complex operator*(const scalar, const complex&);
-        friend complex operator*(const complex&, const scalar);
-        friend complex operator/(const complex&, const scalar);
-        friend complex operator/(const scalar, const complex&);
+        friend complex operator*(const scalar s, const complex& c);
+        friend complex operator*(const complex& c, const scalar s);
+        friend complex operator/(const complex& c, const scalar s);
+        friend complex operator/(const scalar s, const complex& c);
 
 
-    // IOstream operators
-
-        friend Istream& operator>>(Istream&, complex&);
-        friend Ostream& operator<<(Ostream&, const complex&);
+    // IOstream Operators
 
+        friend Istream& operator>>(Istream& is, complex& c);
+        friend Ostream& operator<<(Ostream& os, const complex& c);
 };
 
 
-// * * * * * * * * * * * * * * Global functions  * * * * * * * * * * * * * * //
+// * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * * //
 
-//- Return a string representation of a complex
-word name(const complex&);
 
+//- Return string representation of complex
+word name(const complex& c);
 
 //- Data associated with complex type are contiguous
 template<>
diff --git a/src/OpenFOAM/primitives/complex/complexI.H b/src/OpenFOAM/primitives/complex/complexI.H
index 346f7a192a..7104ac84b7 100644
--- a/src/OpenFOAM/primitives/complex/complexI.H
+++ b/src/OpenFOAM/primitives/complex/complexI.H
@@ -2,10 +2,10 @@
   =========                 |
   \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
    \\    /   O peration     |
-    \\  /    A nd           |
+    \\  /    A nd           | Copyright (C) 2019 OpenCFD Ltd.
      \\/     M anipulation  |
 -------------------------------------------------------------------------------
-                            | Copyright (C) 2011-2016 OpenFOAM Foundation
+                            | Copyright (C) 2011-2014 OpenFOAM Foundation
 -------------------------------------------------------------------------------
 License
     This file is part of OpenFOAM.
@@ -25,51 +25,75 @@ License
 
 \*---------------------------------------------------------------------------*/
 
-// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
-
-namespace Foam
-{
-
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-inline complex::complex()
+inline constexpr Foam::complex::complex() noexcept
+:
+    re(0),
+    im(0)
 {}
 
 
-inline complex::complex(const scalar Re, const scalar Im)
+inline constexpr Foam::complex::complex(const Foam::zero) noexcept
 :
-    re(Re),
-    im(Im)
+    re(0),
+    im(0)
+{}
+
+
+inline constexpr Foam::complex::complex(const scalar r) noexcept
+:
+    re(r),
+    im(0)
+{}
+
+
+inline constexpr Foam::complex::complex(const scalar r, const scalar i) noexcept
+:
+    re(r),
+    im(i)
 {}
 
 
 // * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
-inline scalar complex::Re() const
+inline void Foam::complex::real(scalar val)
+{
+    re = val;
+}
+
+
+inline void Foam::complex::imag(scalar val)
+{
+    im = val;
+}
+
+
+inline Foam::scalar Foam::complex::Re() const
 {
     return re;
 }
 
 
-inline scalar complex::Im() const
+inline Foam::scalar Foam::complex::Im() const
 {
     return im;
 }
 
 
-inline scalar& complex::Re()
+inline Foam::scalar& Foam::complex::Re()
 {
     return re;
 }
 
 
-inline scalar& complex::Im()
+inline Foam::scalar& Foam::complex::Im()
 {
     return im;
 }
 
 
-inline complex complex::conjugate() const
+inline Foam::complex Foam::complex::conjugate() const
 {
     return complex(re, -im);
 }
@@ -77,85 +101,98 @@ inline complex complex::conjugate() const
 
 // * * * * * * * * * * * * * * * Member Operators  * * * * * * * * * * * * * //
 
-inline void complex::operator=(const complex& c)
+inline void Foam::complex::operator=(const complex& c)
 {
     re = c.re;
     im = c.im;
 }
 
 
-inline void complex::operator+=(const complex& c)
+inline void Foam::complex::operator=(const Foam::zero)
+{
+    re = 0;
+    im = 0;
+}
+
+
+inline void Foam::complex::operator+=(const complex& c)
 {
     re += c.re;
     im += c.im;
 }
 
 
-inline void complex::operator-=(const complex& c)
+inline void Foam::complex::operator-=(const complex& c)
 {
     re -= c.re;
     im -= c.im;
 }
 
 
-inline void complex::operator*=(const complex& c)
+inline void Foam::complex::operator*=(const complex& c)
 {
     *this = (*this)*c;
 }
 
 
-inline void complex::operator/=(const complex& c)
+inline void Foam::complex::operator/=(const complex& c)
 {
     *this = *this/c;
 }
 
 
-inline void complex::operator=(const scalar s)
+inline void Foam::complex::operator=(const scalar s)
 {
     re = s;
-    im = 0.0;
+    im = 0;
 }
 
 
-inline void complex::operator+=(const scalar s)
+inline void Foam::complex::operator+=(const scalar s)
 {
     re += s;
 }
 
 
-inline void complex::operator-=(const scalar s)
+inline void Foam::complex::operator-=(const scalar s)
 {
     re -= s;
 }
 
 
-inline void complex::operator*=(const scalar s)
+inline void Foam::complex::operator*=(const scalar s)
 {
     re *= s;
     im *= s;
 }
 
 
-inline void complex::operator/=(const scalar s)
+inline void Foam::complex::operator/=(const scalar s)
 {
     re /= s;
     im /= s;
 }
 
 
-inline complex complex::operator!() const
+inline Foam::complex Foam::complex::operator~() const
 {
     return conjugate();
 }
 
 
-inline bool complex::operator==(const complex& c) const
+inline Foam::complex Foam::complex::operator!() const
+{
+    return conjugate();
+}
+
+
+inline bool Foam::complex::operator==(const complex& c) const
 {
     return (equal(re, c.re) && equal(im, c.im));
 }
 
 
-inline bool complex::operator!=(const complex& c) const
+inline bool Foam::complex::operator!=(const complex& c) const
 {
     return !operator==(c);
 }
@@ -164,47 +201,46 @@ inline bool complex::operator!=(const complex& c) const
 // * * * * * * * * * * * * * * * Friend Functions  * * * * * * * * * * * * * //
 
 
+namespace Foam
+{
+
 inline scalar magSqr(const complex& c)
 {
     return (c.re*c.re + c.im*c.im);
 }
 
 
+inline scalar mag(const complex& c)
+{
+    return sqrt(magSqr(c)); // OR std::hypot(c.re, c.im);
+}
+
+
 inline complex sqr(const complex& c)
 {
     return c * c;
 }
 
 
-inline scalar mag(const complex& c)
+inline const complex& min(const complex& c1, const complex& c2)
 {
-    return sqrt(magSqr(c));
+    if (magSqr(c1) < magSqr(c2))
+    {
+        return c1;
+    }
+
+    return c2;
 }
 
 
 inline const complex& max(const complex& c1, const complex& c2)
 {
-    if (mag(c1) > mag(c2))
-    {
-        return c1;
-    }
-    else
+    if (magSqr(c1) < magSqr(c2))
     {
         return c2;
     }
-}
 
-
-inline const complex& min(const complex& c1, const complex& c2)
-{
-    if (mag(c1) < mag(c2))
-    {
-        return c1;
-    }
-    else
-    {
-        return c2;
-    }
+    return c1;
 }
 
 
@@ -220,8 +256,7 @@ inline const complex& sum(const complex& c)
 }
 
 
-template<class Cmpt>
-class Tensor;
+template<class Cmpt> class Tensor;
 
 inline complex transform(const Tensor<scalar>&, const complex c)
 {
@@ -273,7 +308,7 @@ inline complex operator*(const complex& c1, const complex& c2)
 
 inline complex operator/(const complex& c1, const complex& c2)
 {
-    scalar sqrC2 = magSqr(c2);
+    const scalar sqrC2 = magSqr(c2);
 
     return complex
     (
diff --git a/src/randomProcesses/processes/UOprocess/UOprocess.C b/src/randomProcesses/processes/UOprocess/UOprocess.C
index 67f3d07d13..0df0a1491c 100644
--- a/src/randomProcesses/processes/UOprocess/UOprocess.C
+++ b/src/randomProcesses/processes/UOprocess/UOprocess.C
@@ -51,7 +51,6 @@ complexVector UOprocess::WeinerProcess()
 
 // * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
-// from components
 UOprocess::UOprocess
 (
     const Kmesh& kmesh,
@@ -85,12 +84,7 @@ UOprocess::UOprocess
         }
         else
         {
-            UOfield[i] = complexVector
-            (
-                complex(0, 0),
-                complex(0, 0),
-                complex(0, 0)
-            );
+            UOfield[i] = complexVector::zero;
         }
     }
 }