Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Express the Following Complex Number in the Standard Form a + I B: 1 ( 2 + I ) 2 - Mathematics

Express the following complex number in the standard form a + i b:

$\frac{1}{(2 + i )^2}$

#### Solution

$\frac{1}{\left( 2 + i \right)^2}$

$= \frac{1}{4 + i^2 + 4i} \left( \because i^2 = - 1 \right)$

$= \frac{1}{3 + 4i}$

$= \frac{1}{3 + 4i} \times \frac{3 - 4i}{3 - 4i}$

$= \frac{3 - 4i}{9 - 16 i^2}$

$= \frac{3 - 4i}{9 + 16}$

$= \frac{3}{25} - \frac{4}{25}i$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Exercise 13.2 | Q 1.03 | Page 31