Question

Please help! May someone please explain step by step how to solve? My parents said I have about ten minutes to tell them the answer or they'll take my phone >.< I also want to understand though so please explain why it is the answer ♥
Find the quotient \[\frac{ x^1 }{ x^2 }\] of the complex numbers. Leave answer in polar form.
\[z1=\sqrt{3}\left[ \cos \frac{ 7\pi }{ 4} +1 \sin \frac{ 7\pi }{ 4 } \right]\]
\[z1=\sqrt{6}\left[ \cos \frac{ 9\pi }{ 4} +1 \sin \frac{ 9\pi }{ 4 } \right]\]

Answer 1

\[[z1=\sqrt{3}\left[ \cos \frac{ 7\pi }{ 4} +1 \sin \frac{ 7\pi }{ 4 } \right]\]

\[z1=\sqrt{6}\left[ \cos \frac{ 9\pi }{ 4} +1 \sin \frac{ 9\pi }{ 4 } \right]\]

Answer 2

sorry...the 1 is actually an imaginary number (i) >.< I don't have my glasses...

Answer 3

:( so they took your phone?

Answer 4

HINT: \(\Large r\left[\cos(x)+i\sin (x)\right] = re^{ix}\)

Answer 5

So for \(\Large\dfrac{z_1}{z_2}\),
you have \(\Large \dfrac{r_1 e^{ix_1}}{r_2e^{ix_2}} = \dfrac{r_1}{r_2}e^{i(x_1-x_2)} = \dfrac{r_1}{r_2}[\cos(x_1-x_2)+i\sin(x_1-x_2)]\)

sorry if it looks complicated, hope it helps and you will get your phone back D:

Answer 6

@AngelCriner

Answer 7

yes they did /.\ and I'm just seeing this I'm so sorry, thank you for explaining still! ♥