Answer :

Let, (a + ib)2 = -4 - 3i


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


a2 + (bi)2 + 2abi = -4 -3i


Since i2 = -1


a2 - b2 + 2abi = -4 - 3i


now, separating real and complex parts, we get


a2 - b2 = -4…………..eq.1


2ab = -3…….. eq.2


a =


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


– b2 = -4


9 – 4b4 = -16b2


4b4 - 16b2 - 9= 0


Simplify and get the value of b2 , we get,


b2 = or b2 = -2


As b is real no. so, b2 =


b= or b= -


Therefore , a= - or a=


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


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