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Unformatted text preview: MATH 135 Solutions to Assignment 9 W12 This assignment is due at 8:30 a.m. on March 24 in the drop box outside the Tutorial Centre, MC 4067. Remember to show all of your computational work. 1. [ 4 marks total: 2 marks for each of (a) and (b) ] Express each of the following complex numbers in polar form. (a) πi Answer : πi = π cos π 2 + i sin π 2 (b) 2 √ 3 + i 2 Answer : We recall that √ 3+ i 2 = cos 5 π 6 + i sin 5 π 6 , so 2 √ 3 + i 2 = 4 cos 5 π 6 + i sin 5 π 6 . 2. [ 6 marks total: 2 marks for each of (a), (b), and (c) ] Express each of the following complex numbers in standard form ( x + iy ). (a) 5(cos 4 π 3 + i sin 4 π 3 ) Answer : 5 cos 4 π 3 + i sin 4 π 3 = 5 1 2 i √ 3 2 ! = 5 2 i 5 √ 3 2 (b) √ 2(cos 9 π 4 + i sin 9 π 4 ) Answer : √ 2 cos 9 π 4 + i sin 9 π 4 = √ 2 1 √ 2 + i 1 √ 2 = 1 + i (c) 2 e i 7 π 4 Answer : 2 e i 7 π 4 = 2 cos 7 π 4 + i sin 7 π 4 = 2 1 √ 2 i 1 √ 2 = √ 2 i √ 2 3. [ 5 marks ] Express (2 i 2 √ 3) 101 in standard form....
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This note was uploaded on 04/13/2010 for the course MATH 135 taught by Professor Andrewchilds during the Spring '08 term at Waterloo.
 Spring '08
 ANDREWCHILDS
 Math

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