find the square root of
- 5+12i
- -4-3i
1).
Let
⇒ 5 + 12 i = (x + iy)2
⇒ 5 + 12 i = x2 - y2 + 2i xy
⇒ 5 + 12 i = (x2 - y2) + 2i xy
⇒ x2 - y2 = 5 ... (1)
and 2xy = 12 .... (2)
Now,
Solving equation (1) and (3),
x2 = 9 and y2 = 4
⇒ x = ± 3 and y = ± 2
From equation (2), 2xy is positve, so x and y are of the same sign.
∴ x = 3, y = 2 or x = – 3, y = -2
2).
Similarly, you can find out the square root of -4-3i.