Answer
Isosceles triangle
Work Step by Step
It is a well-known fact that when dealing with complex numbers, a complex conjugate can be defined as a different complex number that shares the same real part as the original one and an identical imaginary part but with an opposite sign.
Let $w$ be the complex conjugate of $z=a+b\textbf{i}$.
Then $w=a-b\textbf{i}$
Now, the modulus of $z$ is :
$||\textbf{z}|| = \sqrt {a^{2} + b^{2}}$
The modulus of $w$ is: $||\textbf{w}|| = \sqrt {a^{2} + (-b)^{2}}=\sqrt{a^2+b^2}$
It is a known fact that the modulus of a complex number refers to the distance between the origin and that number on the complex plane. Considering that the distance from the origin to the given points is equal, if we were to draw a triangle using these points and the origin, both sides of the triangle would be equal due to the same modulus. As a result of having two equal sides in the triangle, we can conclude that it is an isosceles triangle.
