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Algebra of Complex Numbers

Let z being...

Question

Let $z$ being a non-zero complex number such that $| z | = 1$ then find the value of $∣ ∣ z^{- 1} ∣ ∣$ .

1

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2

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3

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none of these

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Solution

The correct option is D $1$
Given, for the non-zero complex number $z$ such that $| z | = 1$ ......(1)
Now,
$∣ ∣ z^{- 1} ∣ ∣$
$= ∣ ∣ ∣ \frac{1}{z} ∣ ∣ ∣$
$= \frac{1}{| z |}$
$= 1$ [ Using (1)]

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