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
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.
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