Find all the complex squareroot s of w81cos 30 degree i sin

Find all the complex squareroot s of w=81(cos 30 degree + i sin 30 degree). Write the roots in polar form with theta in degrees. Find all the complex squareroot s of w = 81 (cos 30 degree + i sin 30 degree) Write the roots in polar form with 0 in degrees.

Solution

w = 81*[cos pi/6 + i*sin pi/6]

Using De-Moivre\'s law

Square root of w = Zo = 9*[cos(pi/12) + i*sin(pi/12)]

Polar form = Zo = 9*e^(i*pi/12)