Let, (a + ib)2 = 16 -30i
Now using, (a + b)2 = a2 + b2 + 2ab
⇒ a2 + (bi)2 + 2abi = 16 - 30i
Since i2 = -1
⇒ a2 - b2 + 2abi = 16 - 30i
Now, separating real and complex parts, we get
⇒ a2 - b2 = 16…………..eq.1
⇒ 2ab = - 30…….. eq.2
⇒ a = -15/b
Now, using the value of a in eq.1, we get
⇒ \((-\frac{15}{b})^2\) – b2 = 16
⇒ 225 – b4 = 16b2
⇒ b4 +16b2 - 225= 0
Simplify and get the value of b2 we get,
b2 = -25 or b2 = 9
As b is real no. so, b2 = 9
b = 3 or b = -3
Therefore, a = - 5 or a = 5
Hence the square root of the complex no. is - 5 + 3i and 5 - 3i.