# Complex number

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• October 16th 2009, 05:03 AM
pankaj
Complex number
1.Let $z$ be a complex number such that $|z| = 1.$

Find the minimum and maximum value of

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

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

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

What does the equation

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

denote geometrically.
• October 16th 2009, 07:59 AM
Deadstar
Perhaps use the triangle equality for part 1.

|z + w| <= |z| + |w| would help you find the max.