First slide

Geometry of complex numbers

Question

Suppose that three points $z_{1}, z_{2}, z_{3}$ are connected by the relation $a z_{1} + b z_{2} + c z_{3} = 0,$ where $a + b +$ $c = 0$ then the points are

Moderate

A

vertices of a right triangle
B

vertices of an isosceles triangle
C

vertices of an equilateral triangle
D

collinear

Solution

$z_{3} = - \frac{1}{c} (a z_{1} + b z_{2}) = \frac{a z_{1} + b z_{2}}{a + b}$

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