- #1

- 782

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## Homework Statement

Prove

[tex]|Re(z)| + |Im(z)| \le \sqrt{2}|z|[/tex]

## The Attempt at a Solution

I was going to try to get from the LHS to RHS

I can only see squaring then square-rooting the LHS and somehow getting to

something involving [tex]\sqrt{|Re(z)|^2 + |Im(z)|^2}[/tex] to recover |z|, but I don't see it... any hints?