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4.1 complex nubers — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS4.1 complex nubers1 Mark
MCQ
The points $1 + 3i,\,5 + i$ and $3 + 2i$ in the complex plane are
  • A
    Vertices of a right angled triangle
  • ✓
    Collinear
  • C
    Vertices of an obtuse angled triangle
  • D
    Vertices of an equilateral triangle
✓

Answer

Correct option: B.
Collinear
b
(b) Let ${z_1} = 1 + 3i,{z_2} = 5 + i$ and ${z_3} = 3 + 2i$
Then area of triangle
$A = \frac{1}{2}\left| {\begin{array}{*{20}{c}}{{x_1}}&{{y_1}}&1\\{{x_2}}&{{y_2}}&1\\{{x_3}}&{{y_3}}&1\end{array}} \right| = \frac{1}{2}\left| {\begin{array}{*{20}{c}}1&3&1\\5&1&1\\3&2&1\end{array}} \right| = 0$
Hence ${z_1},{z_2}$ and ${z_3}$ are collinear.

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