First slide

Algebra of complex numbers

Question

If |z| $\geq$ 5, then least value of $|z - \frac{1}{z}|$ is

Moderate

A

5
B

24/5
C

8
D

8/3

Solution

As |z| ≥ 5, $|\frac{1}{z}| \leq \frac{1}{5}$ Now,
$|z - \frac{1}{z}| \geq | | z |- \frac{1}{| z |}| = | z | - \frac{1}{| z |} \geq 5 - \frac{1}{5} = \frac{24}{5}$
The least value is attained when z = 5.

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