Find the value of $\frac{w+1}{1-w}$ given that $w^2=-1$

Question

Question

There is a new real number $w$ such that $w^2 = -1$. If all the laws of arithmetic applies, find the value of $\dfrac{w+1}{1-w}$ .

I tried the following:

$$\frac{w+1}{1-w} = \frac{(w+1)^2}{(1-w)(w+1)} = \frac{2w}{2} = w$$

Then I got stuck... how do I evaluate $w$ (for the test I just put the answer $\sqrt{-1}$. Is this answer correct?

Answer 1

The answer is quite simply $w.$ One can show readily that $-w$ is also a square root of $-1,$ so $\sqrt{-1}$ is ambiguous.