SOLUTION: If z = x+iy , z³-z²= 4+8i then z=.....

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Question 1205770: If z = x+iy
, z³-z²= 4+8i then z=.....
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

I can guess one possible value of z mentally

    z = -2i.


Then  z%5E3 = %28-2i%29%5E3 = -8%2Ai%28i%5E2%29 = (-8)*i*(-1) = 8i

and

      z%5E2 = %28-2i%29%5E2 = 4%2Ai%5E2 = -4,

so

    z%5E3 - z%5E2 = 8i + 4 = 4 + 8i.

Solved (one value of z is guessed).