Search any question & find its solution
Question:
Answered & Verified by Expert
If $z=x+i y$, then show that $z \bar{z}+2(z+\bar{z})+b=0$, where $b \in R$, represents a circle.
Solution:
2670 Upvotes
Verified Answer
We have $z=x+i y$
Then $\bar{z}=x-i y$
Now, $z \bar{z}+2(z+\bar{z})+b=0$
$$
\Rightarrow(x+i y)(x-i y)+2(x+i y+x-i y)+b=0
$$
$\Rightarrow x^2+y^2+4 x+b=0$, which is the equation of a circle.
Then $\bar{z}=x-i y$
Now, $z \bar{z}+2(z+\bar{z})+b=0$
$$
\Rightarrow(x+i y)(x-i y)+2(x+i y+x-i y)+b=0
$$
$\Rightarrow x^2+y^2+4 x+b=0$, which is the equation of a circle.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.