- #1
latentcorpse
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What's the set [tex]\{ z \in \mathbb{C}| |z|^2 \geq z+ \bar{z} \}[/tex]?
I've set z=a+ib and found [tex]a^2 + b^2 \geq 2a \Rightarrow b^2 \geq a(2-a)[/tex]
I'm not sure how to interpret this geometrically ie what it looks like?
I suppose it is the set of vectors whose length is bigger than twice their real part. I guess if I take the square root then I find [tex]\{ b \geq \pm \sqrt{a} \} \cap \{ b \geq \pm \sqrt{2-a} \}[/tex]
How do we draw this?
Thanks.
I've set z=a+ib and found [tex]a^2 + b^2 \geq 2a \Rightarrow b^2 \geq a(2-a)[/tex]
I'm not sure how to interpret this geometrically ie what it looks like?
I suppose it is the set of vectors whose length is bigger than twice their real part. I guess if I take the square root then I find [tex]\{ b \geq \pm \sqrt{a} \} \cap \{ b \geq \pm \sqrt{2-a} \}[/tex]
How do we draw this?
Thanks.