# Generalized uncertainty principle

So I'm working on the proof of the generalized uncertainty principle and there is a step that I'm not fully understanding. There is a line were it says that for any complex number we can write the inequality as [Re(z)]^2 + [Im(z)]^2 >/ [Im(z)]^2. why are we able to get rid of the real part on the left hand side?

Does this have anything to do with the magnitude being greater than the magnitude of the imaginary part?

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Both $\text{Re}[z]$ and $\text{Im}[z]$ are real numbers. When you square them you will get positive numbers (or zero). When you add two positive numbers together, you definitely get a number that is larger than either of the two.