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

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

Tardigrade Admin · Accepted Answer

Let z1 = 1 + i, z2 = - 2 + 3i and z3 = 0 + (5/3) i Then |x1&y1&1 x2&y2&1 x3&y3&1| = |1&1&1 -2&3&1 0&5/3&1| = 1(3- (5/3)) + 1(2) +1((-10/3)) = (4/3) + 2 - (10/3) = (4+6-10/3) =0

Q. The points represented by the complex numbers $1 + i, - 2 + 3 i, \frac{5}{3} i$ on the argand plane are

vertices of an equilateral triangle

vertices of an isosceles triangle

collinear

None of these

Let $z_{1} = 1 + i, z_{2} = - 2 + 3 i$ and $z_{3} = 0 + \frac{5}{3} i$
Then $∣ ∣ x_{1} x_{2} x_{3} y_{1} y_{2} y_{3} 111 ∣ ∣ = ∣ ∣ 1 - 2 0 13 5/3 111 ∣ ∣$
$= 1 (3 - \frac{5}{3}) + 1 (2) + 1 (\frac{- 10}{3})$
$= \frac{4}{3} + 2 - \frac{10}{3}$
$= \frac{4 + 6 - 10}{3} = 0$

Q. The points represented by the complex numbers 1+i,−2+3i,35​i on the argand plane are