Complex NumbersHard

Question

If z = x + iy and z1/3 = a - ib then = k(a2 - b2) where k =

Options

A.1
B.2
C.3
D.4

Solution

z1/3 = a - ib
z = (a - ib)3
x + iy = (a3 - 3ab2) + i(b3 - 3a2b)
= a2 - 3b2           = b2 - 3a2
= 4(a2 - b2)    k = 4

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