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Properties of Modulus

If | z - 1|...

Question

If $| z - 1 | = 2$ , then the value of $z ¯ ¯ ¯ z - z - ¯ ¯ ¯ z$ is equal to:

- 3

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4

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3

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- 4

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Solution

The correct option is C $3$
Given $| z - 1 | = 2$
we know that $| z |^{2} = z . ¯ z$
so taking square root on both side.
$| z - 1 |^{2} = 4$
$(z - 1) (¯ z - 1) = 4$
$(z - 1) (¯ z - 1) = 4$
$z . ¯ z - ¯ z - z + 1 = 4$
$z . ¯ z - z - ¯ z = 3$
so answer is 3.

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