The set $C = \{ z:z\overline{z} + a\overline{z} + \overline{a}z + b = 0,\ b \in R$ and $b

Question

The set $C = \{ z:z\overline{z} + a\overline{z} + \overline{a}z + b = 0,\ b \in R$ and $b < |a|^{2}\}$ is

Dr. Abubacker · Accepted Answer

(b)
Given, $C = \{ z:z\overline{z} + a\overline{z} + \overline{a}z + b = 0,\ \ \ b \in R$ and $b < |a|^{2}\}$
Since, $z\overline{z} + a\overline{z} + \overline{a}z + b = 0,\ \ \ b \in R$ represents circle having centre at $–a$ and radius $\sqrt{|a|^{2} - b}$
Then, $z$ lies on the circle having infinite points
Hence, $C$ represents infinite sets

Q. The set $C = \{ z:z\overline{z} + a\overline{z} + \overline{a}z + b = 0,\ b \in R$ and $b < |a|^{2}\}$ is

Explanation

Reviewed by Dr. Abubacker

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