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## Homework Statement

prove that sqrt2|z| greater than or equal to |Rez| + |Imz|

## Homework Equations

|z|^2 = x^2 + y^2

Rez=x, Imz=y

## The Attempt at a Solution

so far I've worked it down to this.

2(x^2 + y^2) greater than or equal to x^2 + 2xy + y^2

I've used a few different values for x and y and it holds true but i don't know if that right or that's how it should be written.

any input would be appreciated.

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