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.