Ask Questions, Get Answers

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

Prove that the triangle formed by the points representing the complex numbers $(10+8i),(-2+4i)$ and $(-11+31i)$ on the Argand plane is right angled.

Can you answer this question?

1 Answer

0 votes
  • If $z_1=x_1+iy_1$ and $z_2=x_2+iy_2$ are represented by the points $A(x_1,y_1),B(x_2,y_2)$ on the Argand plane,their $AB=\mid z_1-z_2\mid$ that on $OA=\mid z_1\mid,OB=\mid z_2\mid$
Step 1:
Let $z_1=10+8i,z_2=-2+4i,z_3=-11+31i$ be represented by the points $A,B,C$ is the Argand plane.
$AB=\mid z_1-z_2\mid=\mid (10+2)+(8-4)i\mid$
$\qquad\quad\qquad\;\;=\mid 12+4i\mid$
Step 2:
$BC=\mid z_2-z_3\mid=\mid (-2+11)+(4-31)i\mid$
$\qquad\quad\qquad\;\;=\mid 9-27i\mid$
Step 3:
$CA=\mid z_3-z_1\mid=\mid (-11-10)+(31-8)i\mid$
$\qquad\quad\qquad\;\;=\mid -21+23i\mid$
Step 4:
Now $AB^2+BC^2=160+810=970$
$AB^2+BC^2=AC^2\Rightarrow ABC$ is a right triangle,right angled at B.
answered Jun 10, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App