Did I do these right??
1.
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2.
What are the solutions to x^3=−2−2i in polar form?
Problem #1: you handled the constants correctly; however, the angles should be subtracted, not divided.
Problem #2: r = sqrt( (-2)2 + (-2)2 ) = sqrt( 4 + 4 ) = sqrt(8)
angle = tan-1( -2 / -2 ) = tan-1( 1 ) = 5pi/4
To find the primary cube root, find the cube root of the r value and divide the angle by 3.
To find the next cube root, the r value remains the same but you need to add 2pi/3 to the angle.
To find the last cube root, the r value remains the same but you need to add another 2pi/3 to the angle.