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Question

If |z21|=|z|2+1, then z lies on

A
a circle
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B
an ellipse
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C
a parabola
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D
a straight line
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Solution

The correct option is D a straight line
Let z=x+iy. Then
|z21|=|z|2+1|(x2y21)+2ixy|=x2+y2+1(x2y21)2+4x2y2=(x2+y2+1)2(x2y21)2(x2+y2+1)2+4x2y2=0(2x2)(2y22)+4x2y2=04x2=0x=0

Hence, z lies on imaginary axis.

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