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Question

If ω=zzi3and|ω|=1, then locus of z is:

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Solution

Given,
w=zzi3
|w|=1
w=x+iyx+iyi3
=x+iyx+i(y13)
|w|=x2+y2x2+(y13)2
1=x2+y2x2+(y13)2
x2+(y13)2=x2+y2

On squaring on both sides, we get,
x2+(y13)2=x2+y2
y2+192y3=y2
19=2y3

y=16 is the locus of z.

Hence, this is the answer.

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