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 ±