Question

Find all the complex square roots of w= 36(cos60°+ isin60°). Write the roots in polar form with θ in degrees.

Answer 1

3√3+i3

Explanation:

w= 36(cos60°+ isin60°)

√w =
`w^(1/2)`=√36(cos60°+ isin60°)

=6√(cos60°+ isin60°)

now using DeMoivre's theorem

=(cos60°+ isin60°)^{1/2}

=(cos60°/2+ isin60°/2)=(cos30°+ isin30°)

w^{1/2}=6(cos30°+ isin30°)

=6(sqrt3/2+i1/2)
`\sqrt{frac{3}{2} }`

=3√3+i3