Q30 of 29 Page 5

If z1 is a complex number other than -1 such that |z1|=1 and , then show that the real parts of z2 is zero.

Given:


⇒


Let us assume z1 = x + iy


⇒ |Z �1|=1


⇒


⇒ x2+y2=1-------------------(1)


⇒


⇒


⇒


⇒


⇒


We know that i2=-1


⇒


⇒


⇒


⇒


⇒


∴ z2 is an imaginary one.


Hence real part of z2 is zero.


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