Q Find the square root of the complex number 5 -12i.

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

Now,

Solving equation (1) and (2),

x2 = 9 and y2 = 4

x = ± 3 and y = ± 2

From equation (1), 2xy is negative, so x and y are of opposite signs.

x = 3, y = – 2 or x = – 3, y = 2

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