If `z_(0),z_(1)` represent points P and Q on the circle `|z-1|=1` taken in anticlockwise sense such that the line segment PQ subtends a right angle at the center of the circle, then `z_(1)=`

Options

A. `1+i(z_(0)-1)`
B. `iz_(0)`
C. `1-i(z_(0)-1)`
D. `i(z_(0)-1)`

Answer

A

Explanation

We have,
`anglePCQ=pi/2`,
`rArr` CQ is obtained by rotating CP through `pi//2` in anticlockwise sense.

`rArr z_(1)-1 = (|z_(1)-1|)/(|z_(0)-1|)(z_(0)-1)e^(ipi//2)`
`rAr z_(1)-1=(z_(0)-1)i` `[therefore |z_(1)-1|=|z_(0)-1|` = radius]
`rArr z_(1)=1+i(z_(0)-1)`