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Hi.
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 z1 = (-1+(1-a2)1/2)/a
It then states that for |a| < 1 , z1 lies inside the unit circle.
Should this be obvious just by looking at z1 ? 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
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 z1 = (-1+(1-a2)1/2)/a
It then states that for |a| < 1 , z1 lies inside the unit circle.
Should this be obvious just by looking at z1 ? 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