Question: Please answer the following question on complex numbers: [Maximum mark: 22] (a) Let = = x +iy be any non-zero complex number. (i) Express in

Please answer the following question on complex numbers:

[Maximum mark: 22] (a) Let = = x +iy be any non-zero complex number. (i) Express in the form utiv. (ii) If = +-= k, ke R, show that either y = 0 or x + y =1. Z (iii) Show that if x2 + y? = 1 then |k s2. [8 marks]

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