F09MTH141ComplexNumbersPracticeQuestions

F09MTH141ComplexNumbersPracticeQuestions - 1 F09 MTH 141...

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Unformatted text preview: 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 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 ....
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This note was uploaded on 09/24/2011 for the course MTH 141 taught by Professor Poliakov during the Fall '10 term at Ryerson.

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F09MTH141ComplexNumbersPracticeQuestions - 1 F09 MTH 141...

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