Question

simplify (1-2i)^5 using de moivres theorem

Answer 1

first write \(1-2i\) in the form \(r(\cos(\theta)+i\sin(\theta))\) then multiply \(\theta \) by 5 and raise \(r\) to the power of 5

Answer 2

\[r=\sqrt{a^2+b^2}=\sqrt{1+4}=\sqrt{5}\]

Answer 3

how do i get it in the form r(cos(θ)+isin(θ))

Answer 4

\[\theta=\tan^{-1}(\frac{b}{a})=\tan^{-1}(-2)\] use a calculator
in general it is not true that \(\theta =\tan^{-1}(\frac{b}{a})\) unless you are in quadrant 1 or 4, but you are in quadrant 4 so it is ok

Answer 5

i wrote the method for finding \(\theta\) and \(r\) now it is a computation
use a calculator to raise to the power of 5

Answer 6

i will have to go and do some research on quadrants cos i have no idea what you are talking about :(