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Modulus of a Complex Number

If z= 2-i i...

Question

If $z = \frac{2 - i}{i}$ , then $R e (z^{2}) + I m (z^{2})$ is equal to

A

1

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B

- 1

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C

2

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D

- 2

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E

3

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Solution

The correct option is A $1$
$z = \frac{2 - i}{i} \Rightarrow z^{2} = \frac{{(2 - i)}^{2}}{i^{2}} = 4 i - 3$
$R e (z^{2}) = - 3; l m (z^{2}) = 4$
$∴ R e (z^{2}) + l m (z^{2}) = - 3 + 4 = 1 | z + 1 | < | z - 1 |$

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