1.

If z is a point on the Argand plane such that |z-1|=1, then (z-2)/z is equal to

Answer»

TAN(arg)Z
cot(arg z)
itan (arg z)
NONE of these

Solution :We have, `|z-1|=1`
So, LET `z-1=costheta+isintheta`
`rArr z-2=sintheta//2(-sintheta//2+icostheta/2)`
and `z=2costheta//2(costheta//2+isintheta//2)`
and, `z=2costheta//2(costheta//2+isintheta//2)`
`rArr (z-2)/(z)=i{(costheta/2+isintheta/2)/(costheta/2+isintheta/2)}tantheta/2`
`rArr (z-2)/z = itantheta/2 rArr (z-2)/z=i tan(arg z)`


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