Simple representation of a complex number

Construct a Complex number with imaginary value only

imaginary 1 --> { re = 0, im = 1 }

Construct a Complex number with real value only

real 1 --> { re = 1, im = 0 }

The complex zero

Add two complex numbers

add (real 1) (imaginary 2) --> { re = 1, im = 2 }

Subtract two complex numbers

subtract { re = 1, im = 2 } (real 2) --> { re = -1, im = 2 }

Multiply two complex numbers

multiply (imaginary 1) (real 2) --> { re = 0, im = 2 }

Divide a complex number by a real number. Notice that the divisor is given first.

real 2 |> divideByReal 2 --> { re = 1, im = 0 }

Check equality of two complex numbers

Given complex number z, computes e^z

The absolute value of complex number, which is also its distance from zero

computes the conjugate of a complex number

conjugate { re = 1, im = 1 } --> { re = 1, im = -1 }