IB MATHEMATICS Topic : Complex Numbers – Multiplying and Dividing Complex Numbers

Complex numbers can be expressed in two forms:

Coordinate form:

and

Polar form

Multiplying Complex Numbers

The rules for multiplying and dividing complex numbers follow the normal rules of arithmetic.
Ifandthen we expand brackets
Ifandare in polar form then we multiply the magnitudes R-1 and R_2 and add the arguments, which are also the exponents.

Dividing Complex Numbers
Ifandthen we make the denominator real by multiplying by the complex conjugate of the denominator

Ifandare in polar form then we divide the magnitudesandand add the arguments, which are also the exponents.

Example: Find the product and quotient ofand


Example: Find the product and quotient ofand