Let z be a complex number having the arg...

Let `z` be a complex number having the argument `theta` ,`0` <` theta` < `pi/2`, and satisfying the equation` |z-3i|=3.` Then find the value of `cottheta-6/z`

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`|z-3i|=3`
So, z lies on circle having centre 3i and radius 3.
Let `z=r(costheta+isintheta)`
Now, `r=OA sintheta=6sintheta`
`implies" "z=6sintheta(costheta+isintheta)`
or `(6)/(z)=(1)/(sintheta(costheta+isintheta))`
`=(costheta-isintheta)/(sintheta)`
`=-i+cottheta`
or `cottheta-(6)/(z)=i`

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