Complex NumbersHard
Question
If z = x + iy and z1/3 = a - ib then 
= k(a2 - b2) where k =
= 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
z = (a - ib)3
x + iy = (a3 - 3ab2) + i(b3 - 3a2b)
= a2 - 3b2 = b2 - 3a2= 4(a2 - b2) k = 4Create a free account to view solution
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