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Question

If x+iy(x,yr, x1/2), the number of values of z satisfying |z|n=(z2+z)|z|n2+1(nN,n>1) is

A
1
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B
2
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C
3
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Solution

The correct option is A 1
The given equation is
|z|n=(z2+z)|z|n2+1
z2+z is real
z2+z=¯z2+¯z
(z¯z)(z+¯z+1)=0
z=¯z=xasz+¯z+10(x1/2)
Hence, the given equation reduces to
xn=xn+x|x|n2+1
x|x|n2=1
x=1
So number of solutions is 1.

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