Question: (a) Let3+ and 2 = a + bi be complex numbers. Suppose that 7 Argument = 12' find Argument(22). 7-2 (b) Let the map

(a) Let3+ and 2 = a + bi be complex numbers. Suppose that 7 Argument = 12' find Argument(22). 7-2 (b) Let the map f: CC be defined by f(z) = Find f() if=1+2i. 1 (c) Solve the equation -12 i(9-2), giving the answer in the form + iy when I, y R. (d) Simplify the expression = -2 (e) Find the cubic root of 1. (f) For=22+4i and 6-8i, find the modulus and argument of w. W (g) The following complex numbers are given, 12-21, and 23 = a + bi, if 2123=16, find the modulus of 23. (h) Given that = 2e satisfies the equation = a(1+3). Find the value of a (i) Evaluate (1+i)8 (j) Find the values of x and y in the equation + I iy 3 2+i 2 i 1- 2VER 2. Using mathematical induction, (a) Prove that 13+23+33 +4 n(n+1) 4 (b) Show that n+2n is divisible by 3.

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