Complex numbers

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

Form of a complex number

Complex numbers take this form:

$$x+yi$$

This can also rewritten as $x+iy$ and (rarely) $yi+x$ or $iy+x$.

Real part

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

Imaginary part

The imaginary part of a complex number $x+yi$ is $y$. It is the coefficient of $i$ (and the vertical coordinate on an Argand diagram).

Equality of complex numbers

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