Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  TN XII Math  >>  Complex Numbers
0 votes

$P$ represents the variable complex number $z$.Find the locus of $P$,if $\mid 2z-3\mid=2$

This is the fourth part of the multi-part Q8.

Can you answer this question?

1 Answer

0 votes
  • If $z=a+ib$ then $\bar{z}=a-ib$.
  • $\mid z\mid=\sqrt{a^2+b^2}$
  • $z^{-1}=\large\frac{a-ib}{a^2+b^2}$
  • $z\bar{z}=a^2+b^2$
  • Also $Re(z)=a,Im(z)=b$
Step 1:
Let $z=x+iy$
$\mid 2z-3\mid=2$
$\mid 2(x+iy)-3\mid=2$
$\Rightarrow \mid (2x-3)+2yi\mid=2$
Step 2:
On squaring both sides
$\mid (2x-3)+2yi\mid^2=4$
Step 3:
The locus of $P$ is a circle with centre at $(\large\frac{3}{2}$$,0)$ .
The locus of $P$ is a circle with centre at $(\large\frac{3}{2}$$,0)$ and radius $1$unit. .
answered Jun 10, 2013 by sreemathi.v
Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App