A complex number. See Internal Representation for more details.

Construct a complex number from real and imaginary parts.

Construct a complex number from magnitude and angle.

Construct a real number.

Construct an imaginary number.

A complex "not a number" value.

nan == divide (complex 0 0) (complex 0 0)

Complex infinity. Infinity is 'very near' large complex numbers defined on the Riemann sphere.

infinity == divide (complex 1 0) (complex 0 0)

Zero as a complex number.

zero == complex 0 0

One as a complex number.

unity == complex 1 0

Test if a complex number is infinite.

isInfinite infinity == True


isInfinite nan == False


isInfinite (complex 1 6) == False

Note: you can also use c == infinity to test for infinity values.

Test if a complex number is not a number.

isNan nan == True


isNan infinity == False


isNan (complex 1 6) == False

Note: you could use c == nan to check for NaN values but it is not recommended as this behavour is different to that of floats (as 0/0 /= 0/0).

Add two complex numbers.

add (complex 4 1) (complex 1 -7) == complex 5 -6

Subtract the second argument (rhs) from the first (lhs).

subtract (complex 8 2) (complex 2 3) == complex 6 -1

Multiply two complex numbers.

multiply (complex 0 4) (complex 1 2) == complex -8 4

Divide the first argument (lhs) by the (rhs).

multiply (complex -12 4.5) (complex 3 0) == complex -4 1.5

Raise the first argument (lhs) to the power of the second (rhs).

pow (imaginary 2) (real 4) == real 16

Raise a complex number to the power of e.

exp (imaginary pi) == real -1 -- allowing for floating point rounding errors .

Compute natural logarithm of a complex number.

log (real -10) == complex 2.302585 pi -- allowing for floating point rounding errors.

Compute the conjugate of a complex number

conjugate (complex 6 8) == complex 6 -8

Get real and imaginary parts of a complex number.

toCartesian (complex 4 7) == { re = 4, im = 7 }


toCartesian (divide (real 1) (real 0)) == { re = 1 / 0, im = 1 / 0 }

Get absolute value and argument of a complex number.

toPolar (complex 4 7) == { abs = 8.0622577, arg = 0.5191461 } -- allowing for floating point rounding errors.


toPolar (divide (real 1) (real 0)) == { abs = 1 / 0, arg = 0 / 0 }

Convert to string.

toString (complex 5 1) == "5+i"

Create a complex number from a string.

Strings must consist of

• optionally: a float possibly including a sign
• zero or one of
  • the character 'i'.
  • a sign followed by the character 'i'
  • a sign followed by another float followed by the character 'i'.

Whitespace is allowed anywhere between the real part and imaginary parts and between the imaginary part and the character 'i'.

fromString "4 + 6i" == Just (complex 4 6)