Complex numbers

10 The complex number w is given by w = −0.5+ i0.5(3)^1/2
(i) Find the modulus and argument of w. [2]
(ii) The complex number zhas modulus R and argument θ, where −(1/3)π < θ <( 1/3)π. State the modulus and argument of wz and the modulus and argument of z/w. [4]
(iii) Hence explain why, in an Argand diagram, the points representing z, wzand z/w are the vertices of an equilateral triangle. [2]
(iv) In an Argand diagram, the vertices of an equilateral triangle lie on a circle with centre at the origin. One of the vertices represents the complex number 4 + 2i. Find the complex numbers represented by the other two vertices. Give your answers in the form x + iy, where x and y are real and exact.

Hi guys can anyone help me to understand part 3 and 4 please. Thanks

A few ways of imagining iii. Put the 3 numbers of interest in polar form, they should all have magnitude R, so will lie on a circle of radius R. What should the arguments be so that the interior angles are all 60 degrees?