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Let f(z) is of the form alpha z +beta , ...

Let f(z) is of the form `alpha z +beta` , where `alpha, beta,z` are complex numbers such that `|alpha| ne |beta|`.f(z) satisfies following properties :
(i)If imaginary part of z is non zero, then `f(z)+bar(f(z)) = f(barz)+ bar(f(z))`
(ii)If real part of of z is zero , then `f(z)+bar(f(z)) =0`
(iii)If z is real , then `bar(f(z)) f(z) gt (z+1)^2 AA z in R`
`(4x^2)/((f(1)-f(-1))^2)+y^2/((f(0))^2)=1 , x , y in R`, in (x,y) plane will represent :

A

hyperbola

B

circle

C

ellipse

D

pair of line

Text Solution

Verified by Experts

The correct Answer is:
A
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