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A1 - of the roots of 2 x 3 3 x 2 2 x[2 4 Let x = 2 3 y =...

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MAT 1341 Assignment 1 due: 11 May Answer each question clearly and legibly. Be sure to explain your reasoning and show your work. It is your responsibility to convince the marker that you understand why your solution is correct. Staple your assignment. Please do not hand in loose sheets, folded over corners, etc. 1. Evaluate each expression, giving your answer in Cartesian form a + bi where a, b R . [8] a) (2 + 3 i ) - (1 - i ) + 3 b) 3 + 4 i + | 3 + 4 i | c) ( - 1 + i )(2 + i ) d) 2 + i 2 - i 2. Give a real polynomial that has both 1 + i and 7 as roots. [2] 3. Find explicitly
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Unformatted text preview: of the roots of 2 x 3 + 3 x 2 + 2 x . [2] 4. Let x = 2 3 , y = 1-1 1 and z = -3 3-3 . [6] a) Find proj y ( x ), the projection of x onto y . b) Find proj z ( x ), the projection of x onto z . c) Find the angle between x and y . 5. Let u , v , w be arbitrary vectors in R 3 . Prove that ( u + v ) · w = u · w + v · w . Note that it is not [4] enough to check an example, you must prove it in general. Show your steps! [ /22] 1...
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