Multiplication of complex number in rectangular (or Cartesian) form, can be simply performed using normal algebra multiplication method.
However, when the complex numbers are in Polar form, their product is found through a special formula. This polar formula enables multiplication to be simple, instead of transforming them to rectangular form before computation.
Polar Formula: A ÐK0 x B ÐY0 = AB Ð(K + Y)0
NOTE: The amplitudes are multiplied together while their arguments are added.
The formula can be proven using trigonometry.
4 Ð100 x 2 Ð450 = (4 x 2) Ð(10 + 45)0 = 8 Ð550
This is a faster way of multiplying complex number. This is better than converting to the rectangular form, which is tedious and time consuming, as well as more prone to mistakes.
Addition Tips on Polar Multiplication
If we are to multiply A ÐK0 a few times, or do a (A ÐK0)n, we can apply the below theorem, which will simplify the mathematical process.
De Moivre's Theorem: (A ÐK0)n = (A)n ÐnK0
This formula is an expansion of the steps dealt with at the beginning of this post.
With this coverage of Multiplication of Polar Complex Number, you are on the way to solve complex number in any form that the mathematics questions are presented. :)
For details on Complex Number Division, click here.
For details on Complex Number Addition, click here.
For details on Forms of Complex Number, click here.