# Product of complex numbers in polar form

• Jul 18th 2011, 05:15 PM
jbwtucker
Product of complex numbers in polar form
Two complex numbers, $\displaystyle z_{1}$ and $\displaystyle z_{2}$, are expressed in polar form.

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

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

A. $\displaystyle (3\sqrt{2},25^{\circ})$
B. $\displaystyle (4, 25^{\circ})$
C. $\displaystyle (3\sqrt{2},150^{\circ})$
D. $\displaystyle (4, 150^{\circ})$
• Jul 18th 2011, 07:48 PM
mr fantastic
Re: Product of complex numbers in polar form
Quote:

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

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

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

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

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 ....?
• Jul 18th 2011, 08:13 PM
jbwtucker
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...

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

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

Thanks for the nudge.
• Jul 19th 2011, 12:21 AM
Siron
Re: Product of complex numbers in polar form
Correct!
• Jul 19th 2011, 08:03 AM
HallsofIvy
Re: Product of complex numbers in polar form
In general, $\displaystyle $$r_1e^{i\theta_1}$$$$r_2e^{i\theta_2}$$= (r_1r_2)e^{i(\theta_1+ \theta_2)}$