Question

I want to use De Moivre’s Theorem to compute (sqrt(3) + i)^4, but I need help finding the right value for theta to use.

Answer 1

\[a+bi=r\cos(\theta)+r\sin(\theta)i\]so we get:\[r=\sqrt{a^2+b^2}\]\[\tan(\theta)=\frac{b}{a}\]

Answer 2

in your case \(a=\sqrt{3}\), \(b=1\)

Answer 3

do you understand?

Answer 4

remember \(e^{ir\theta}=r(\cos(\theta)+i\sin(\theta))\)

Answer 5

ok, thanks!

Answer 6

yw