Question

Raise this number to its power using the DeMoivre's theorem: (square root3+i)^5

Answer 1

DeMoivre's theorem says
\[(\cos x + i \sin x)^{n} = \cos (nx) + i \sin (nx)\]
So you need to figure out the magnitude and angle of the number first. The new magnitude will be the old magnitude to the 5th power, and the new angle will be the old angle times 5. Then, probably convert that back to a complex number (a + bi).

Use the Pythagorean Theorem to get the magnitude. Use tan = opposite/adjacent to get the angle.