IB MATHEMATICS Topic ; Complex Numbers – Polar and Coordinate Forms of Complex Numbers – Argand Diagrams

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