How do you sketch Re(z^2)>1?

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Question:

How do you sketch Re(z^2)>1?

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[tex]z=x+iy\implies z^2=x^2-y^2+2ixy\implies \mathrm{Re}(z^2)=x^2-y^2[/tex]If you're familiar with the conic sections, you should recognize this as a hyperbola.

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