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

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

(i) â€“ 5 + 12i

(ii) -7 â€“ 24i

(iii) 1 â€“ i

(iv) â€“ 8 â€“ 6i

(v) 8 â€“ 15i

(vi)

(vii)

(viii) 4i

(ix) -i

Solution:

If b > 0,

If b < 0,

(i) â€“ 5 + 12i

Given:

â€“ 5 + 12i

We know, Z = a + ib

So,

Here, b > 0

Let us simplify now,

âˆ´ Square root of (â€“ 5 + 12i) is Â±[2 + 3i]

(ii) -7 â€“ 24i

Given:

-7 â€“ 24i

We know, Z = -7 â€“ 24i

So,

Here, b < 0

Let us simplify now,

âˆ´ Square root of (-7 â€“ 24i) is Â± [3 â€“ 4i]

(iii) 1 â€“ i

Given:

1 â€“ i

We know, Z = (1 â€“ i)

So,

Here, b < 0

Let us simplify now,

âˆ´ Square root of (1 â€“ i) is Â±

(iv) -8 -6i

Given:

-8 -6i

We know, Z = -8 -6i

So,  = -8 -6i

Here, b < 0

Let us simplify now,

âˆ´ Square root of (-8 -6i) is Â± [1 â€“ 3i]

(v) 8 â€“ 15i

Given:

8 â€“ 15i

We know, Z = 8 â€“ 15i

So,   = 8 â€“ 15i

Here, b < 0

Let us simplify now,

âˆ´ Square root of (8 â€“ 15i) is Â±

(vi)

Given:

We know, Z =

So,

= -11 â€“ 60i

Here, b < 0

Let us simplify now,

âˆ´ Square root of () is Â± (5 â€“ 6i)

(vii)

Given:

We know, Z =

So,

Here, b > 0

Let us simplify now,

âˆ´ Square root of  is Â±

(viii) 4i

Given:

4i

We know, Z = 4i

So,  = 4i

Here, b > 0

Let us simplify now,

âˆ´ Square root of 4i is Â±

(ix) â€“i

Given:

-i

We know, Z = -i

So,  = -i

Here, b < 0

Let us simplify now,

âˆ´ Square root of â€“i is Â±

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