Question

The points represented by the complex numbers 1+i,-2+3i,(5)/(3)i on the Argand plane are:

• A. vertices of an equilateral triangle
• B. vertices of an isosceles triangle
• C. collinear
• D. None of these

Hint:

Equal slopes between pairs of points indicate collinearity.

Answer 1

The Correct Option is C

Step 1: Represent points: 1+i → (1,1), -2+3i → (-2,3), (5)/(3)i → (0,(5)/(3)).
Step 2: Slope between (1,1) and (-2,3): m=(3-1)/(-2-1)=-(2)/(3)
Step 3: Slope between (1,1) and (0,(5)/(3)): m=((5)/(3)-1)/(0-1)=-(2)/(3)
Step 4: Since slopes are equal, points are collinear.