complex,complex!
Algebra
Level
3
If z is a point on the Argand plane such that |z-1|=1,then
((z-2)/z) is equal to ?
i tan(arg(z))
i cot(arg(z))
tan(arg(z))
cot(arg(z))
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1 solution
|z-1|=1 . Let z-1=cos(x)+isin(x).
z-2=-1+cos(x)+isin(x) and z=1+cos(x)+isin(x)
z-2=2sin(x/2)(-sin(x/2)+icos(x/2))
and z=2cos(x/2)(cos(x/2)+isin(x/2)). Divide both!