Multiplying Complex Numbers

The multiplication of complex numbers is realized by applying the distributive property and taking into account that i2 = −1.

(a + bi) · (c + di) = (ac − bd) + (ad + bc)i

(5 + 2 i) · (2 − 3 i) =

= 10 − 15i + 4i − 6 i2 = 10 − 11i + 6 = 16 − 11i


Polar Form

The multiplication of two complex numbers is another complex number such that:

The modulus is the product of the modules.

Its argument is the sum of the arguments.

Complex Number Polar Form

645° · 315° = 1860°

Multiplication by a Complex Number of Module 1

The multiplication of a complex number z = rα for 1β is rotated at angle β around the origin.

rα · 1β = rα + β

Multiplication by a Complex Number of Module 1