diff --git a/src/Magnum/Math/Complex.h b/src/Magnum/Math/Complex.h
index 5372469f0..b299edbee 100644
--- a/src/Magnum/Math/Complex.h
+++ b/src/Magnum/Math/Complex.h
@@ -43,6 +43,8 @@ namespace Implementation {
     template<class T> constexpr static Complex<T> complexFromMatrix(const Matrix2x2<T>& matrix) {
         return {matrix[0][0], matrix[0][1]};
     }
+
+    template<class, class> struct ComplexConverter;
 }
 
 /** @relatesalso Complex
@@ -159,6 +161,14 @@ template<class T> class Complex {
          */
         constexpr explicit Complex(const Vector2<T>& vector): _real(vector.x()), _imaginary(vector.y()) {}
 
+        /** @brief Construct complex number from external representation */
+        template<class U, class V = decltype(Implementation::ComplexConverter<T, U>::from(std::declval<U>()))> constexpr explicit Complex(const U& other): Complex{Implementation::ComplexConverter<T, U>::from(other)} {}
+
+        /** @brief Convert complex number to external representation */
+        template<class U, class V = decltype(Implementation::ComplexConverter<T, U>::to(std::declval<Complex<T>>()))> constexpr explicit operator U() const {
+            return Implementation::ComplexConverter<T, U>::to(*this);
+        }
+
         /** @brief Equality comparison */
         bool operator==(const Complex<T>& other) const {
             return TypeTraits<T>::equals(_real, other._real) &&
diff --git a/src/Magnum/Math/Test/ComplexTest.cpp b/src/Magnum/Math/Test/ComplexTest.cpp
index 43ba7ce18..32ab90a1b 100644
--- a/src/Magnum/Math/Test/ComplexTest.cpp
+++ b/src/Magnum/Math/Test/ComplexTest.cpp
@@ -29,7 +29,27 @@
 #include "Magnum/Math/Complex.h"
 #include "Magnum/Math/Matrix3.h"
 
-namespace Magnum { namespace Math { namespace Test {
+struct Cmpl {
+    float re, im;
+};
+
+namespace Magnum { namespace Math {
+
+namespace Implementation {
+
+template<> struct ComplexConverter<Float, Cmpl> {
+    constexpr static Complex<Float> from(const Cmpl& other) {
+        return {other.re, other.im};
+    }
+
+    constexpr static Cmpl to(const Complex<Float>& other) {
+        return {other.real(), other.imaginary()};
+    }
+};
+
+}
+
+namespace Test {
 
 struct ComplexTest: Corrade::TestSuite::Tester {
     explicit ComplexTest();
@@ -38,6 +58,7 @@ struct ComplexTest: Corrade::TestSuite::Tester {
     void constructDefault();
     void constructFromVector();
     void constructCopy();
+    void convert();
 
     void compare();
     void isNormalized();
@@ -69,6 +90,7 @@ ComplexTest::ComplexTest() {
               &ComplexTest::constructDefault,
               &ComplexTest::constructFromVector,
               &ComplexTest::constructCopy,
+              &ComplexTest::convert,
 
               &ComplexTest::compare,
               &ComplexTest::isNormalized,
@@ -138,6 +160,22 @@ void ComplexTest::constructCopy() {
     CORRADE_COMPARE(b, Complex(2.5f, -5.0f));
 }
 
+void ComplexTest::convert() {
+    constexpr Cmpl a{1.5f, -3.5f};
+    constexpr Complex b{1.5f, -3.5f};
+
+    constexpr Complex c(a);
+    CORRADE_COMPARE(c, b);
+
+    constexpr Cmpl d(b);
+    CORRADE_COMPARE(d.re, a.re);
+    CORRADE_COMPARE(d.im, a.im);
+
+    /* Implicit conversion is not allowed */
+    CORRADE_VERIFY(!(std::is_convertible<Cmpl, Complex>::value));
+    CORRADE_VERIFY(!(std::is_convertible<Complex, Cmpl>::value));
+}
+
 void ComplexTest::compare() {
     CORRADE_VERIFY(Complex(3.7f, -1.0f+TypeTraits<Float>::epsilon()/2) == Complex(3.7f, -1.0f));
     CORRADE_VERIFY(Complex(3.7f, -1.0f+TypeTraits<Float>::epsilon()*2) != Complex(3.7f, -1.0f));