Question

Fourth roots of 16(cos280 degrees+isin280 degrees)

Answer 1

\[z = 16 (\cos 280 + i \sin 280) = 16 cis 280\] Find z^(1/4)
Use de Moivre's formula.\[( \cos x + i \sin x)^n = \cos (nx) + isin (nx)\]

Answer 2

You need to remember to multiply by \(r^n\) also.

Answer 3

Like so:\[z^n=(r(\cos \theta + i \sin \theta))^n = r^n \cdot (\cos n\theta + i \sin n\theta)\]

Answer 4

Yeah, good point =)