Short answers:

Q1) Part C (II)

C. Let z = 5e^3πi / 8.

I. Express 1/z^2 in the form x + yi, where x, ye R.

II. Find all rational values of k such that z is purely real.

Q3 A. Show that there are no real solutions to the equation et = sec x+i cosec x .

B. i. Express ie^it in modulus argument form.

ii. Find all integers n such that (sin x+icos x)" = sin nx+cos nx is true for all xe R.

C. Let z=(x + yi)³-1li, where x, y, z Z.

Using the result in Question 7 (b) (i), or otherwise

I. show that 11= y(3x² - y²).

II. Hence, find z.