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Complex numbers

A complex number is a number which contains both an imaginary part and a real part.

Form of a complex number

Section titled “Form of a complex number”

Complex numbers take this form:

This can also rewritten as and (rarely) or .

Real part

Section titled “Real part”

The real part of a complex number is . It is the number without an term, and is the number we are used to using in everyday maths.

Imaginary part

Section titled “Imaginary part”

The imaginary part of a complex number is . It is the coefficient of (and the vertical coordinate on an Argand diagram).

Equality of complex numbers

Section titled “Equality of complex numbers”

Two complex numbers are equal if both their real and imaginary parts are equal.