find maximum and minimum value of $|z|$ If $a,b,c$ are complex number of equal magnitude and satisfy $az^2+bz+c=0,$ 
then finding maximum and minimum value of $|z|$
with the help of triangle inequality $|az^2+bz+c|\leq |az^2|+|bz|+|c|=|a||z|^2+|b||z|+|c|$
now let $|a|=|b| = |c| = k>0$
so $|az^2+bz+c|\leq k(|z|^2+|z|+1)$
so $|z|^2+|z|+1\geq 0$
wan,t be able to go after that, help me

Hints:


*

*for the maximum value: $\;a z^2 = -bz - c \implies |z|^2 \le |z|+1 \implies |z| \le \cfrac{1+\sqrt{5}}{2}\,$;

*for the minimum value, rewrite the equation as $\;c\cfrac{1}{z^2}+b\;\cfrac{1}{z}+a=0\;$ and use the previous result to show that $\;\cfrac{1}{|z|} \le \cfrac{1+\sqrt{5}}{2} \;\iff\; |z| \ge \cfrac{\sqrt{5}-1}{2}\,$.
