Unimodular Complex Number:
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A complex number z defines that |z| = 1 is called unimodular complex number. Since |z| = 1, z present in a circle of radius 1 unit and centre(0, 0).
If |z| = 1 => z = cosθ + i sinθ,
Þ 1/z = (cosθ + i sinθ)-1 = cosθ - i sinθ
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Illustration: If z1 and z2 are two nonzero complex numbers and 
is a uni-modular then prove that z1/z2 is completely real.
Solution: 
=> P(z1/z2)present on the right bisector of line joining A (i) and B(- i ) that denote P(z1/z2 ) present on real axis. Hence z1/z2 is completely real.
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