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The number of complex numbers z such tha...

The number of complex numbers z such that `|z""""1|""=""|z""+""1|""=""|z""""i|` equals (1) 1 (2) 2 (3) `oo` (4) 0

A

`oo`

B

`0`

C

`1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
Let`z= x +iy`. So
`|z-1| = |z+1| rArr Re(z) =0 rArrx le 0`
`|z -1| = |z + i| rArr x = y`
` |z+1| = |z-i| rArr y = - x`
Only (0,0) will satisfy all conditions.
Therefore, the number of complex numbers(z) is 1.
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