Find the square root of the following complex numbers :
Let ...(i)
Squaring both sides, we get
x2 - y2 + 2xyi ...(ii)
(∵ i2 = -1)
Equating real and imaginary parts, we get
x2 - y2 = 1 ...(iii)
2xy = ...(iv)
4x2y2 = 16(3) = 48
Now, (x2 + y2)2 = (x2 - y2)2 +4x2y2 (x2 + y2)2 = 1 + 48 = 49
x2 + y2 =
7
But, x2 + y2 -7 for x. y
R
x2 + y2 = 7 ...(v)
Also, x2 - y2 = 1
Adding, we get 2x2 = 8 x2 = 4
x =
2
When x = 2, from (iv), y =
Putting in (i), we get
or
Hence,