A complex number is a record of a real part and an imaginary part.

Generates a complex number.

complex 1 2 == 1 + 2 i

The number i

i == complex 0 1

The number 1.

complex 1 0 == one

The number 0.

complex 0 0 == zero

Creates a complex number from one real numer.

fromReal 5 == 5 + 0 i

Provides the real part of a complex number.

real 2 + 3 i == 2

Provides the imaginary part of a complex number.

imaginary 2 + 3 i == 3

Takes the absolute value of a complex number.

abs 2 + 2 i == sqrt 8


abs -2 - 2 i == sqrt 8


abs 0 + 0 i == 0

Returns the conjugate of a complex number

conjugate 2 + 3 i == 2 - 3 i


conjugate 2 - 3 i == 2 + 3 i

Negates a complex number.

negation 1 + 2 i == -1 - 2 i


negation -1 - 2 i == 1 + 2 i


negation -1 + 2 i == 1 - 2 i

Returns the sign of a complex number.

sgn 0 + 0 i == 0


sgn 0 + 2 i == 0


sgn 1 + -10 i == 1


sgn -1 + 10 i == -1


sgn -1 + -10 i == -1

The argument of a complex number. It is in radians. This is also known as the phase or angle.

arg 0 + 0 i == 0


arg 0 + i == pi / 2

Square root of a complex number. Returns only one of two possibilites.

sqrt (2+2i) == (1.55...) + i0.6435..

Adds two complex numbers by adding the real and imaginary parts.

Subtacts two complex numbers by negating and adding.

Multiplies two complex numbers so that

mult (a + bi) (c + di) == (ac - bd) + (ad + bc)

Divides two complex numbers.

div 2 + 2 i 1 + 1 i == 2 + 0


div 2 + 2 i 0 + 0 i == NaN + NaNi

Complex sine.

Complex cosine.

Complex tangent.

Complex inverse sine.

Complex inverse cosine.

Complex inverse tan.

Euler's formula.

       euler 2 == e^{i*2} == cos 2 + i*sin 2

The natrual log of a complex number.

The exponent of a complex number.

Take a complex number to a complex power.

pow 1+0i 2+2i == (1)^{2+2i} == 1