Let, (a + ib)² = -2 + 2i

Now using, (a + b)² = a² + b² + 2ab

a² + (bi)² + 2abi = -2 + 2i

Since i² = -1

a² - b² + 2abi = -2 + 2i

Now, separating real and complex parts, we get

a² - b² = -2…………..eq.1

2ab =2……..eq.2

a =

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

– b² = -2

– b⁴ = -2b²

⁴ - 2b² - 3= 0

Simplify and get the value of b², we get,

b² = -1 or b² = 3

As b is real no. so, b² = 3

b= or b =

Therefore, a= 1 or a= -1

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