In an Argand diagram, the vertices on an equilateral triangle lie on a circle with center at the origin. One of the vertices represents the complex numbers 4 + 2i. Find the complex numbers that represent the other two vertices. Gives your answers in the form x + yi where x and y are real and exact.
[Math] Complex numbers
complex numbers
Best Answer
Hint: We want to rotate the given point $4+2i$ about the origin by $2\pi/3$ ($120$ degrees), and then do it again.
Rotating $z=a+bi$ about the origin (counterclockwise) by the angle $\theta$ is done by multiplying $z$ by $\cos \theta+i\sin\theta$.
Remark: After we have rotated $4+2i$ suitably, we don't really need to do it again. The third vertex can be found by using the fact that the sum of the three vertices is $0$.