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

Question

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

anonymous · Answer

ick

anonymous · Answer

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 $\tan^{-1}(\frac{4}{3})$

anonymous · Answer

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??

anonymous · Answer

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

anonymous · Answer

thanks!