- #1

dyn

- 773

- 61

I have been trying to calculate the real definite integral with limits 2π and 0 of ## 1/(k+sin2θ) ##

To avoid the denominator becoming zero I know this means |k|> 1

Making the substitution ##z= e^{iθ}## eventually ends up giving me a quadratic equation in ##z^2## with 2 pairs of roots given by ##z^2 = i (+\sqrt{k^2-1} - k ) ##

and ## z^2 = i (-\sqrt{k^2-1} -k ) ##

The solution then states that"clearly the 1st two poles lie inside the unit circle and the 2nd two outside". This seems reasonable but how do I know for a fact that it is true ?

Thanks