Question

Find the square root of the following complex numbers.

(i) -11 – 60√-1

(ii) 1 + 4√-3

Answer 1

(i) -11 – 60√-1

Given as

-11 – 60√-1

As we know, Z = -11 – 60√-1

Therefore, √(a + ib) = -11 – 60√-1

= -11 – 60i

Here, b < 0

Now let us simplify now,

Thus, square root of (-11 – 60√-1) is ± (5 – 6i)

(ii) 1 + 4√-3

Given as

1 + 4√-3

As we know, Z = 1 + 4√-3

Therefore, √(a + ib) = 1 + 4√-3

= 1 + 4(√3) (√-1)

= 1 + 4√3i

Here, b > 0

Now let us simplify now,

Thus, square root of (1 + 4√-3) is ± (2 + √3i)