Question

Find the square root of the following complex numbers.

(i) – 8 – 6i

(ii) 8 – 15i

Answer 1

(i) -8 - 6i

Given as

-8 - 6i

As we know, Z = -8 - 6i

Therefore, √(a + ib) = -8 - 6i

Here, b < 0

Now let us simplify now,

= [1^1/2 – i 9^1/2]

= ± [1 – 3i]

Thus, square root of (-8 - 6i) is ± [1 – 3i]

(ii) 8 – 15i

Given as

8 – 15i

As we know, Z = 8 – 15i

Therefore, √(a + ib) = 8 – 15i

Here, b < 0

Now let us simplify now,

Thus, square root of (8 – 15i) is ± 1/√2 (5 – 3i)