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

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 ±