A complex number z may take one of two forms:

Coordinate form:or polar form:

These are both illustrated on the Argand Diagram below.

Polar can be converted to coordinate form and vice versa.

Converting Polar to Coordinate Form

where 'Re' means 'the real part of' and 'Im' means 'the imaginary part of'.

Converting Coordinate to Polar Form

(in radians).

These are just the normal equations for converting polar coordinates into rectangular coordinates and vice versa.