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in Complex Numbers by (29.6k points)
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If z1 is a complex number other than -1 such that |z1| = 1 and Z\(\frac{Z_1-1}{z_1+1}\) then show that the real parts of z2 is zero.

1 Answer

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Best answer

Given

⇒ |Z1| = 1 and Z2 = \(\frac{Z_1-1}{z_1+1}\) 

Let us assume z1=x+iy 

⇒ |Z1|=1

⇒ \(\sqrt{x^2+y^2}=1\)

⇒ x2+y2=1 ..........(1)

We know that i2=-1

∴ z2 is an imaginary one.

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