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Introduction

Here you go: a simple but mathematically rigorous implementation of complex numbers in one small C# library. No problem in square rooting negative numbers anymore!

Functions

Absolute value
Addition
Argument
Conjugation
Cosine
Exponential function
Exponentiation
Division
Hyperbolic functions (Sinh, Cosh, Tanh, Coth, Sech, Csch)
Logarithm
Multiplication
Sine
Square root
Subtraction

Using the code

Either add a reference to CompLib.dll to your project, or directly use the class Complex.cs within your project.

The actual usage is intuitive:

Complex I = Complex.I; // imaginary unit
Complex a = new Complex(1, 3); // inits a = 1+3i
Complex a2 = 1 + 3 * I; // a equals a2

Complex z = Complex.Pow((Complex.Sin(1/(1+I))), 1/3);

Points of interest

One more thing: Complex logarithm is not a unique operation; the main value is computed as is common in the CAS world. E.g., the equation z^4 = -1 has four complex solutions, but only one is returned when trying "z = Complex.Sqrt(Complex.Sqrt(-1));" (as does Maple, for instance). This is due to the computation of the exponentiation:

Pow(a,b) := Exp(b * Log(a))

History

Coming soon

init complex number with format string such as "3+4i" using regex.

Update July 3, 2007 #2

Major bug in Arg() fixed (thanks Petr Stanislav!); this affects Log(), Pow(), and Sqrt().

Update July 3, 2007

Added hyperbolic functions.

Update June 10, 2007

Replaced ^-operator with "public static Complex Pow", similar to Math.Pow.

Update June 7, 2007

Added Zero and One as constants (e.g., use "Complex z = Complex.One;" instead of "Complex z = new Complex(1)").
Major bug of division operation removed (using a/b = a*Conj(b)*(1/(Abs(b)*Abs(b)) now).
ToString method bug fixed.

A C# class for complex numbers