Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

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:

\[\frac{1}{(2 + i )^2}\]

Advertisement Remove all ads

Solution

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

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

\[ = \frac{1}{3 + 4i}\]

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

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

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

\[ = \frac{3}{25} - \frac{4}{25}i\]

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×