Let, (a + ib)2 = -15 - 8i

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

a2 + (bi)2 + 2abi = -15 -8i

Since i2 = -1

a2 - b2 + 2abi = -15 - 8i

Now, separating real and complex parts, we get

a2 - b2 = -15…………..eq.1

2ab = -8…….. eq.2

a =

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

– b2 = -15

16 – b4 = -15b2

b4 - 15b2 - 16= 0

Simplify and get the value of b2 , we get,

b2 = 16 or b2 = -1

As b is real no. so, b2 = 16

b= 4 or b= -4

Therefore , a= -1 or a= 1

Hence the square root of the complex no. is -1 + 4i and 1 - 4i.

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