Question

The points in the argand plane represented by the complex conjugates of $1+2i,2-3i,3-4i$

• A. are collinear
• B. form an equilateral triangle
• C. form an obtuse angled triangle
• D. form an acute angled triangle

Answer 1

Answer: (C)

The complex conjugate of given points are in argand plane $A(1-2i),B(2+3i),C(3+4i)$
So, $a=BC=\sqrt{1+1}=\sqrt{2}$
$b=CA=\sqrt{4+36}=\sqrt{40}$
$c=AB=\sqrt{1+25}=\sqrt{26}$
$\because \cos B=\frac{a^2+c^2-b^2}{2ac}=\frac{2+26-40}{2\sqrt{2}\sqrt{26}}4$
$=-\frac{12}{4\sqrt{13}}=-\frac{3}{\sqrt{13}}<0$
So, point $A,B$ and $C$ represents the vertices of an obtuse angled triangle.