The modulus of the complex quantity $(2 - 3 i) (- 1 + 7 i)$ .

5 \sqrt{13}

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5 \sqrt{26}

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13 \sqrt{5}

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26 \sqrt{5}

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Solution

The correct option is B $5 \sqrt{26}$
The given complex quantity is $(2 - 3 i) (- 1 + 7 i)$ .

Let $z_{1} = 2 - 3 i$ and $z_{2} = - 1 + 7 i$

Therefore, $| z_{1} | = \sqrt{2^{2} + (- 3)^{2}} = \sqrt{13}$

$| z_{2} | = \sqrt{(- 1)^{2} + 7^{2}} = \sqrt{50} = 5 \sqrt{2}$

Thus, required modulus = $| z_{1} z_{2} | = \sqrt{13} \times 5 \sqrt{2} = 5 \sqrt{26}$ .

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(2 - 3 i) (- 1 + 7 i)

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