If z=1 (1-i)(2+3 i) , then |z|= - Vidyadip

MCQ

If $z=\frac{1}{(1-i)(2+3 i)}$, then $|z|=$

A
$1$
✓
$1 / \sqrt{26}$
C
$4 / \sqrt{26}$
D
$5/ \sqrt{26}$

✓

Answer

Correct option: B.

$1 / \sqrt{26}$

$1 / \sqrt{26}$
Let $z =\frac{1}{(1-i)(2+3 i)}$
$\Rightarrow z=\frac{1}{2+i-3 i^2}$
$\Rightarrow z=\frac{1}{2+i+3}$
$\Rightarrow z=\frac{1}{5+i} \times \frac{5-i}{5-i}$
$\Rightarrow z=\frac{5-i}{25-i^2}$
$\Rightarrow z=\frac{5-i}{25+1}$
$\Rightarrow z=\frac{5-i}{26}$
$\Rightarrow z=\frac{5}{26}-\frac{i}{26}$
$\Rightarrow|z|=\sqrt{\frac{25}{676}+\frac{1}{676}}$
$\Rightarrow z=\frac{1}{\sqrt{26}}$

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