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.

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