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Modulus of a Complex Number

Let z = x+i...

Question

Let $z = x + i y$ be a complex number with modulus $m$ . Then the modulus of $3 z$ will be:

9 m

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3 m

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6 m

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m

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Solution

The correct option is B $3 m$
$| z | = \sqrt{x^{2} + y^{2}}$
$| 3 z | = \sqrt{{(3 x)}^{2} + {(3 y)}^{2}} = \sqrt{{9 x}^{2} + 9 y^{2}}$
$∴ | 3 z | = 3 \sqrt{x^{2} + y^{2}} = 3 m$

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