Question

use De Moiver's theorem to find the indicated power of the complex number, write answer in standard form. (3+4i)^20

Answer 1

ick

Answer 2

you have to write 3+4i in trig form first
\[r(\cos(\theta)+i\sin(\theta))\]
\(r\) is easy, it is \(\sqrt{3^2+4^2}=5\) but as for \(\theta\) it is \(\tan^{-1}(\frac{4}{3})\)

Answer 3

so you will have
\[(5^{20}((\cos(20\times \tan^{-1}(\frac{4}{3})+i\sin(20\tan^{-1}(\frac{4}{3}))\] i would use a calculator, because i have no idea what any of these numbers are. are you really expecte to raise 5 to the power of 20??

Answer 4

ok well the final answer im given is 5^20(.95 -.30i)

Answer 5

thanks!