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in Quadratic Equations by (50.7k points)
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If \(\frac{z-1}{z+1}\) is purely imaginary and z = –1, show that |z| = 1.

1 Answer

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Best answer

Let z = a + ib

Given that \(\frac{z-1}{z+1}\) is purely imaginary

⇒ real part = 0

⇒ a2 + b2 - 1 = 0

⇒ a2 + b2 = 1

⇒ |z| = 1

Hence proved.

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