prove that sqrt2|z| greater than or equal to |Rez| + |Imz|
|z|^2 = x^2 + y^2
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.