# If Z = 1 ( 1 − I ) ( 2 + 3 I ) , than | Z | = - Mathematics

MCQ

$\text { If } z = \frac{1}{(1 - i)(2 + 3i)}, \text { than } \left| z \right| =$

#### Options

• 1

• $1/\sqrt{26}$

• $5/\sqrt{26}$

• none of these

#### Solution

$1/\sqrt{26}$

$\text { Let }z = \frac{1}{\left( 1 - i \right)\left( 2 + 3i \right)}$

$\Rightarrow z = \frac{1}{2 + i - 3 i^2}$

$\Rightarrow z = \frac{1}{2 + i + 3}$

$\Rightarrow z=\frac{1}{5 + i}\times\frac{5 - i}{5 - i}$

$\Rightarrow z=\frac{5 - i}{25 - i^2}$

$\Rightarrow z=\frac{5 - i}{25 + 1}$

$\Rightarrow z=\frac{5 - i}{26}$

$\Rightarrow z = \frac{5}{26} - \frac{i}{26}$

$\Rightarrow \left| z \right|=\sqrt{\frac{25}{676} + \frac{1}{676}}$

$\Rightarrow z = \frac{1}{\sqrt{26}}$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Q 22 | Page 65