Related Articles

# Class 11 RD Sharma Solutions – Chapter 13 Complex Numbers – Exercise 13.3

• Last Updated : 21 Feb, 2021

### Question 1. Find the square root of the following complex numbers.

(i) – 5 + 12i

(ii) -7 – 24i

(iii) 1 – i

(iv) – 8 – 6i

(v) 8 – 15i

(vi) (vii) (viii) 4i

(ix) -i

Solution:

If b > 0, If b < 0, (i) – 5 + 12i

Given:

– 5 + 12i

We know, Z = a + ib

So, Here, b > 0

Let us simplify now, ∴ Square root of (– 5 + 12i) is ±[2 + 3i]

(ii) -7 – 24i

Given:

-7 – 24i

We know, Z = -7 – 24i

So, Here, b < 0

Let us simplify now, ∴ Square root of (-7 – 24i) is ± [3 – 4i]

(iii) 1 – i

Given:

1 – i

We know, Z = (1 – i)

So, Here, b < 0

Let us simplify now, ∴ Square root of (1 – i) is ± (iv) -8 -6i

Given:

-8 -6i

We know, Z = -8 -6i

So, = -8 -6i

Here, b < 0

Let us simplify now, ∴ Square root of (-8 -6i) is ± [1 – 3i]

(v) 8 – 15i

Given:

8 – 15i

We know, Z = 8 – 15i

So, = 8 – 15i

Here, b < 0

Let us simplify now, ∴ Square root of (8 – 15i) is ± (vi) Given: We know, Z = So, = -11 – 60i

Here, b < 0

Let us simplify now, ∴ Square root of ( ) is ± (5 – 6i)

(vii) Given: We know, Z = So,  Here, b > 0

Let us simplify now, ∴ Square root of is ± (viii) 4i

Given:

4i

We know, Z = 4i

So, = 4i

Here, b > 0

Let us simplify now, ∴ Square root of 4i is ± (ix) –i

Given:

-i

We know, Z = -i

So, = -i

Here, b < 0

Let us simplify now, ∴ Square root of –i is ± Attention reader! All those who say programming isn’t for kids, just haven’t met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

My Personal Notes arrow_drop_up