Find all the complex roots Leave your answers in polar form

Find all the complex roots. Leave your answers in polar form with the argument in degrees. The complex fourth roots of 25 + 25 squareroot 3 i. z_k = [cos degree + degree k) + i sin degree + degree k)], k = 0, 1, ...,

Solution

z = (25 + 25sqrt3*i) ^1/4

|z| = 50 ; theta = tan^-1(sqrt3) = pi/3

zk = (50^1/4[ cos[(pi/3+2pi*k)/4] +i*sin[(pi/3+2pi*k)/4] ]

= 50^1/4[ cos(pi/12 + pi*k/2) +i*sin(pi/12 + pi*k/2) ]