Exponential Form & de Moivre's Theorem (Edexcel A Level Further Maths: Core Pure): Exam Questions

In an Argand diagram, the points ,  and  are the vertices of an equilateral triangle with its centre at the origin. The point  represents the complex number .

Find the complex numbers represented by the points and , giving your answers in the form , where  and  are real and exact.

The points ,  and  are the midpoints of the sides of triangle .

Find the exact area of triangle .

Use de Moivre’s theorem to prove that

Hence find the distinct roots of the equation

giving your answer to 3 decimal places where appropriate.

A complex number  has modulus 1 and argument .

Show that

Hence, show that