Answer :

Let, (a + ib)2 = 5 + 12i


Now using, (a + b)2 = a2 + b2 + 2ab


a2 + (bi)2 + 2abi = 5 + 12i


Since i2 = -1


a2 - b2 + 2abi = 5 + 12i


now, separating real and complex parts, we get


a2 - b2 = 5…………..eq.1


2ab = 12……..eq.2


a =


now, using the value of a in eq.1, we get


– b2 = 5


36 – b4 = 5b2


b4 + 5b2 - 36= 0


Simplify and get the value of b2, we get,


b2 = -9 or b2 = 4


As b is real no. so, b2 = 4


b = 2 or b= -2


Therefore, a = 3 or a= -3


Hence the square root of the complex no. is 3 + 2i and -3 -2i.


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