Question

Find the square root of the following complex numbers.

(i) – 5 + 12i

(ii) -7 – 24i

(iii) 1 – i

Answer 1

(i) – 5 + 12i

Given as

– 5 + 12i

As we know, Z = a + ib

Therefore, √(a + ib) = √(-5 + 12i)

Here, b > 0

Now let us simplify now,

Thus square root of (– 5 + 12i) is ± [2 + 3i]

(ii) -7 – 24i

Given as

-7 – 24i

As we know, Z = -7 – 24i

Therefore, √(a + ib) = √(-7 – 24i)

Here, b < 0

Now let us simplify now,

Thus square root of (-7 – 24i) is ± [3 – 4i]

(iii) 1 – i

Given as

1 – i

As we know, Z = (1 – i)

Therefore, √(a + ib) = √(1 – i)

Here, b < 0

Now let us simplify now,

Thus square root of (1 – i) is ± [(√(√2 + 1)/2) – i(√(√2 - 1)/2)]