Question

COMPLEX NUMBERS HELP REQUIRED.
*Question attached below* Will give medal :)

Answer 1

Can I have some help with a step-by-step explanation to this question, please?

Answer 2

rewrite "8i" in polar form
\[8i = 8(\cos \theta +i \sin \theta) \rightarrow \theta = \frac{\pi}{2}\]
\[z^3 = 8(\cos \frac{\pi}{2} + i \sin \frac{\pi}{2})\]
now rewrite again in e^i form
\[z^3 = 8 e^{i \pi/2}\]
take 3rd root
\[\large z = 2 e^{\frac{i \pi/2 + 2k \pi}{3}}\]
for k = 0,1,2
\[z = 2 e^{i \pi/6} , 2 e^{i 5\pi/6}, 2 e^{i 3\pi/2}\]

Answer 3

Give me a second to process everything :)

Answer 4

no problem
here is identity for where i took 3rd root
http://en.wikipedia.org/wiki/De_Moivre%27s_formula#Applications

Answer 5

Alrighty. I get it! Thank you so much! :)