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Question

If zāˆ’iz+i(zā‰ āˆ’i) is a purely imaginary number, then z.ĀÆz is equal to

A
1
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B
2
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C
None of these
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Solution

The correct option is A 1

Here ziz+i=x+i(y1x+i(y+1).xi(y+1)xi(y+1)
=(x2+y21)+i(2x)x2+(y+1)2
As ziz+i is purely imaginary, we get
x2+y21=0 x2+y2=1 z¯z=1.


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