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F09MTH141ComplexNumbersPracticeQuestions

# F09MTH141ComplexNumbersPracticeQuestions - 1 F09 MTH 141...

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1 F09 MTH 141 – Linear Algebra– Complex Numbers Practice Questions Question 1 In each part, plot the point and sketch the vector that corresponds to the given complex numbers: (a) 2+3i (b) -3-2i (c) -5i Question 2 In each part find the real numbers x and y . (a) x - iy = - 2 + 3 i (b) ( x + y ) + ( x - y ) i = 3 + i Question 3 Given that z 1 = 1 - 2 i and z 2 = 4 + 5 i , find (a) z 1 - z 2 (b) 3 z 1 + 4 z 2 (c) 1 2 z 1 - 3 2 z 2 Question 4 In each part perform the calculations and express the result in the form a + ib . (a) (2 - i )(3 + i )(4 - 2 i ) (b) (3 - 2 i ) 2 - (3 + 2 i ) 2 (c) (1 + i + i 2 + i 3 ) 100 Question 5 In each part, solve the equation by the quadratic formula and check your result by substituing the solutions into the given equation. (a) z 2 + 2 z + 2 = 0 (b) z 2 - z + 1 = 0

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2 Question 6 (a) Show that if n is a positive integer, the only values for i n are 1 , - 1 , i, - i . (b) Find i 2009 . Question 7 In each part find z and | z | . (a) z = 2 + 7 i (b) z = - i (c) z = - 3 - 5 i Question 8 Given that z 1 = 1 - 5 i and z 2 = 3 + 4 i find: (a) z 1 z 2 (b) z 1 z 2 (c) z 1 | z 2 | Question 9 Given that z 1 = 1 + i and z 2 = 1 - 2 i find: (a) z 1 - z 1 z 2 (b) z 1 - 1 z 2 (c) z
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F09MTH141ComplexNumbersPracticeQuestions - 1 F09 MTH 141...

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