1.Let $\displaystyle z$ be a complex number such that $\displaystyle |z| = 1.$

Find the minimum and maximum value of

$\displaystyle |1 + z| + |1 - z + z^2|$

2.If $\displaystyle a>0$ and $\displaystyle |z+\frac{1}{z}|=a$.

Then find minimum and maximum value of $\displaystyle |z|$

What does the equation

$\displaystyle |z+\frac{1}{z}|=a$

denote geometrically.