# Thread: Product of complex numbers in polar form

1. ## Product of complex numbers in polar form

Two complex numbers, $z_{1}$ and $z_{2}$, are expressed in polar form.

$z_{1}=(\sqrt{2},10^{\circ})$
$z_{2} = (2\sqrt{2}, 15^{\circ})$

What is the product of $z_{1}$ and $z_{2}$?

A. $(3\sqrt{2},25^{\circ})$
B. $(4, 25^{\circ})$
C. $(3\sqrt{2},150^{\circ})$
D. $(4, 150^{\circ})$

2. ## Re: Product of complex numbers in polar form

Originally Posted by jbwtucker
Two complex numbers, $z_{1}$ and $z_{2}$, are expressed in polar form.

$z_{1}=(\sqrt{2},10^{\circ})$
$z_{2} = (2\sqrt{2}, 15^{\circ})$

What is the product of $z_{1}$ and $z_{2}$?

A. $(3\sqrt{2},25^{\circ})$
B. $(4, 25^{\circ})$
C. $(3\sqrt{2},150^{\circ})$
D. $(4, 150^{\circ})$
Have you reviewed the formula (undoubtedly in your class notes or textbook) that says how two multiply two complex numbers written in polar form? What does it say? Therefore ....?

3. ## Re: Product of complex numbers in polar form

Not working from a textbook. Prepping for a state test that covers algebra, trig, pre-calc, calculus, statistics, and probability. The only materials provided by the state are a sample test and some study suggestions.

I was looking for how to multiply complex numbers, didn't add "in polar form" to my search. Googled that, as you suggested, and found that you multiply magnitudes and add angles. So...

$(2)(2\sqrt{2})=4$
$10^{\circ} + 15^{\circ}=25^{\circ}$

So the answer is $(4, 25^{\circ})$, which is B.

Thanks for the nudge.

Correct!

5. ## Re: Product of complex numbers in polar form

In general, $$$r_1e^{i\theta_1}$$$$r_2e^{i\theta_2}$$= (r_1r_2)e^{i(\theta_1+ \theta_2)}$