- #1

- 716

- 49

I have looked through an example of working out a trig integral using the residue theorem. The integral is converted into an integral over the unit circle centred at the origin. The singularities are found.

One of them is z

_{1}= (-1+(1-a

^{2})

^{1/2})/a

It then states that for |a| < 1 , z

_{1}lies inside the unit circle.

Should this be obvious just by looking at z

_{1}? Because I can't see it. I have tried a few values and it seems to be true but that doesn't prove it. If its not obvious how do I go about trying to show it ?

Thanks