find a square root of the complex number

Question. Find a square root of the complex number .

Answer.

Let . By inspection (of i), the modulus of w is 1; we need to find .

where n=2 and k is 0 and 1 (from 0 to n-1).

Therefore there are two numbers w that, when squared, give :

and

The textbook answer, however, only gives one value of w ( ). Am I wrong in thinking that there are two values of w? Or, the question has only asked for one of them ('a square root'), rather than 'find all square roots'?

PS I understand that there are always two numbers (one positive and one negative) that, when squared, give the same number. I only wanted to check whether the same principle applies to the questions about complex numbers.