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Let $a,c \in \mathbb R$ with $a \neq 0$, and let $b \in \mathbb C$. Define $$S=\{z\in \mathbb C: az\bar{z}+b\bar{z}+\bar{b}z+c=0\}.$$

a. Show that $S$ is a circle, if $|b|^2 > ac$. Determine its centre and radius.
b. What is $S$ if $a=0$ and $b \neq 0$?

How would I get started in this? I'm completely stuck. Most appreciated.

  • 2
    Start by writing $z=x+yi$, $b=p+qi$ and expand.2011-10-20

2 Answers 2