RD Sharma Class 11 Solutions Chapter 13 - Complex Numbers (Ex 13.3) Exercise 13.3

• In exercise 13.3 of the RD Sharma class 11 Mathematics, there are a total of 9 questions given on the complex number.

• Solutions of all these 9 questions of exercise 13.3 are given in the PDF file format for the students to download.

• The PDF file is free to download for all the students of class 11, for the Subject of Mathematics.

Solved Examples

1. Find the square root of – 5 + 12i

(i) Given is:

– 5 + 12i

We know that, Z = a + ib

So, √(a + ib) = √(-5+12i)

Here, b > 0

Let us now simplify,

\[\sqrt{-5+12i}= \pm \left [ \left ( \frac{-5+\sqrt{\left ( -5 \right )^{2}+12^{2}}}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+\sqrt{\left ( -5 \right )^{2}+12^{2}}}{2} \right )^{\frac{1}{2}}  \right ]\]

                                                                                                                                       [Since,b>0]

=\[\pm \left [ \left ( \frac{-5+\sqrt{\left ( 25 \right )+144}}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+\sqrt{\left ( 25 \right )+144}}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ \left ( \frac{-5+\sqrt{169}}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+\sqrt{ 169}}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ \left ( \frac{-5+13}{2} \right )^{\frac{1}{2}} +i\left (   \frac{5+13}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ \left ( \frac{8}{2} \right )^{\frac{1}{2}} +i\left (   \frac{18}{2} \right )^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ 4^{\frac{1}{2}} +i9^{\frac{1}{2}}  \right ]\]

= \[\pm \left [ 2+3i \right ]\]

∴ Hence, Square root of (– 5 + 12i) is ±[2 + 3i]

Hence this article is useful for the students to understand the solutions of RD Sharma  Chapter 13 - Complex Numbers (Ex 13.3) Exercise 13.3.