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# A C# class for complex numbers

, 3 Jul 2007 CPOL
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Implementation of the most common functions of complex numbers.

## 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
• 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 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.

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