short answers q1 part c ii c let z 5e 3pi 8 i express 1 z 2 in the for

Question

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.