Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes
and the coefficients of 25 x
2
-x

Answer 1

So I need a little help with the following: Considering separately the cases of real and complex roots show that the roots of the quadratic equation z2+bz+c=0z2+bz+c=0 lie in or on the unit circle (i.e. |zi|≤1|zi|≤1) if and only if |c|≤1|c|≤1 and |b|≤1+c|b|≤1+c, where bb and cc are real coefficients.

I showed both sides of the relation for real roots, but now I am stuck on the complex case. Any ideas?