Question

Someone help me please! Find the product of the complex numbers. Express your answer in trigonometric form.

Answer 1

@zepdrix

Answer 2

I always find it easier to work with these if you write them as complex exponentials,
\[\Large\rm z_1=4\left(\cos\frac{\pi}{3}+\mathcal i\sin\frac{\pi}{3}\right)\]\[\Large\rm z_1=4e^{\mathcal i \pi/3}\]

\[\Large\rm z_2=3\left(\cos\frac{2\pi}{5}+\mathcal i \sin\frac{2\pi}{5}\right)\]\[\Large\rm z_2=3e^{2\pi\mathcal i/5}\]

Answer 3

Have you learned about that, or no? :o

Answer 4

no I did not , so what do i do next??

Answer 5

If you haven't learned about that, then ummm I think the formula for multiplying looks something like this:\[\Large\rm z_1=r_1(\cos \theta_1+\mathcal i \sin \theta_1)\]\[\Large\rm z_2=r_2(\cos \theta_2+\mathcal i \sin \theta_2)\]\[\Large\rm z_1\cdot z_2=r_1 r_2\left(\cos(\theta_1+\theta_2)+\mathcal i \sin(\theta_1+\theta_2)\right)\]

Answer 6

\[\Large\rm z_1\cdot z_2=3\cdot4\left[\cos\left(\frac{\pi}{3}+\frac{2\pi}{5}\right)+\mathcal i \sin \left(\frac{\pi}{3}+\frac{2\pi}{5}\right)\right]\]So we get something like that, yes?
Just need to simplify the radius and new angle.

Answer 7

So is it A?

Answer 8

Mmm yes good.