1 Complex Numbers 1a. [5 marks] Solve . 1b. [3 marks] Show that . 1c. [9 marks] Let . Find the modulus and argument of in terms of . Express each answer in its simplest form. 1d. [5 marks] Hence find the cube roots of in modulus-argument form. 2. [4 marks] In the following Argand diagram the point A represents the complex number and the point B represents the complex number . The shape of ABCD is a square. Determine the complex numbers represented by the points C and D. 3a. [6 marks] Find three distinct roots of the equation giving your answers in modulus- argument form.
2 3b. [3 marks] The roots are represented by the vertices of a triangle in an Argand diagram. Show that the area of the triangle is . 4a. [6 marks] (i) Use the binomial theorem to expand . (ii) Hence use De Moivre’s theorem to prove (iii) State a similar expression for in terms of and . 4b. [4 marks] Let , where is measured in degrees, be the solution of which has the smallest positive argument.
- Fall '18
- Complex number, Use De Moivre’s theorem