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. $\displaystyle (4, 150^{\circ})$

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 ....?

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.

Re: Product of complex numbers in polar form

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)}$