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

(a) Use de Moivre’s theorem to prove that

(b) Hence find the distinct roots of the equation

giving your answer to 3 decimal places where appropriate.

The infinite series C and S are defined by

Given that the series C and S are both convergent,

a) show that

(b) Hence show that

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 .

(a) 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 .

(b) Find the exact area of triangle .