Let, (a + ib)2 = - 7 + 24i
Now using, (a + b)2 = a2 + b2 + 2ab
a2 + (bi)2 + 2abi = -7 + 24i
Since i2 = -1
a2 - b2 + 2abi = -7 + 24i
Now, separating real and complex parts, we get
⇒ a2 - b2 = - 7…………..eq.1
⇒ 2ab = 24…….. eq.2
⇒ a = 12/b
Now, using the value of a in eq.1, we get
⇒ (12/b)2 – b2 = - 7
⇒ 144 – b4 = -7b2
⇒ b4 - 7b2 - 144 = 0
Simplify and get the value of b2, we get,
⇒ b2 = - 9 or b2 = 16
As b is real no. so, b2 = 16
b = 4 or b = - 4
Therefore, a = 3 or a = - 3
Hence the square root of the complex no. is 3 + 4i and - 3 - 4i.