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Question

Find all non-zero complex number Z satisfying ¯¯¯¯Z=iZ2.

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Solution

Let, Z=x+iy.
Given,
¯¯¯¯Z=iZ2
or, xiy=i(x2y2+2ixy)
Comparing the real and imaginary part both sides we get,
x=2yx and y=x2y2.......(1).
or, y=12[ Since Z is non-zero].
Using the value of y in (1) we get,
x2=34
or, x=±32
So Z=(±32,12).

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