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If 'z, lies on the circle |z-2i|=2sqrt...

If 'z, lies on the circle `|z-2i|=2sqrt2`, then the value of `arg((z-2)/(z+2))` is the equal to

A

`(pi)/(3)`

B

`(pi)/(4)`

C

`(pi)/(6)`

D

`(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B

`CA=CB=2sqrt(2)" " OC=2rArr OA=OB=2`
`rArr A=2+0i, B=-2+0i`
Clearly, `angleBCA=(pi)/(2)`
`rArr angle BPA=(pi)/(4)rArr arg ((z-2)/(z+2))=(pi)/(4)`
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