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complex numbers assignment 5 - Assignment 5 Complex Numbers...

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Assignment 5: Complex Numbers Due: 12 th Novemeber Name: _________________ 1. Let z = x + y i. Find the values of x and y if (1 – i) z = 1 3i. Working: Answer: ………………………………………….. (Total 4 marks) 3. Let z 1 = 2 2 i 6 - , and z 2 = 1 – i. (a) Write z 1 and z 2 in the form r (cos θ + i sin θ ), where r > 0 and 2 π θ 2 π . (6) (b) Show that 2 1 z z = cos 12 π + i sin 12 π . (2) (c) Find the value of 2 1 z z in the form a + b i, where a and b are to be determined exactly in radical (surd) form. Hence or otherwise find the exact values of cos 12 π and sin 12 π . (4) (Total 12 marks) 1
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5. Let z 1 = a + 4 sin i 4 cos π π and z 2 = b . 3 sin i 3 cos + π π Express 3 2 1 z z in the form z = x + y i . Working: Answer: .................................................................. (Total 3 marks) 2
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7. If z is a complex number and | z + 16| = 4 | z + l|, find the value of | z| . Working: Answer: .................................................................. (Total 3 marks) 9. Find the values of a and b , where a and b are real, given that ( a + b i)(2 – i) = 5 – i.
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