# Math Help - Complex number problem

1. ## Complex number problem

for any complex number z prove that - I z I < or equal to Re (z) < or equal to I z I

2. ## Re: Complex number problem

Originally Posted by purpeil
for any complex number z prove that $- | z |\le Re (z) \le |z|$
If each of $a~\&~b$ is a real number: \begin{align*} a^2 &\le a^2+b^2\\|a| &\le \sqrt{a^2+b^2}\end{align*} .

Let $a=\text{Re}(z)~\&~b=\text{Im}(z)$ you are done.