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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

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Solution

\[1/\sqrt{26}\]

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

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

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

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

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

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

\[\Rightarrow z=\frac{5 - i}{26}\]

\[\Rightarrow z = \frac{5}{26} - \frac{i}{26}\]

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

\[\Rightarrow z = \frac{1}{\sqrt{26}}\]

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APPEARS IN

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