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(i) Let z be a non-real complex number lying on the circle |z|=1. Then prove that z= (1+ I tan (("arg" z)/(2)))/(1-I tan(("arg"z )/(2))) (ii) Find the modulus and the argument of the complex number z_1, where z_1 = z^2 - z and z = cos theta+I sin theta.

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Answer :(II) `|z_1| =2|sin THETA//2|, "ARG" (z_1) = (pi+3 theta)/(2` or `|z_1|=0`, "arg" (z_1)` is not defined


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