Consider the two complex numbers z and w...

Consider the two complex numbers z and w, such that
`w=(z-1)/(z+2)=a+ib, " where " a,b in R " and " i=sqrt(-1).`
If `z=CiStheta`, which of the following does hold good?

A

(a) `sin theta=(9b)/(1-4a)`

B

(b) `cos theta=(1-5a)/(1+4a)`

C

(c) `(1+5a)^(2)+(3b)^(2)=(1-4a)^(2)`

D

(d) All of these

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The correct Answer is:

C

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