P p 7 6 a2 b z1 z1 z1 64z1 641 3i 64 64 3i p 2 a2

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Unformatted text preview: z1 = 26 cos(6( ⇡ /3)) + i sin(6( ⇡ /3)) = 64(1 + 0i) = 64. p p 7 6 A2 (b): z1 = z1 z1 = 64z1 = 64(1 3i) = 64 64 3i p 2 A2 (c): z2 has absolute value 02FRASER UNIVERSITY argument ⇡ /2: Dr. Marni MISHNA, Department of Mathematics, SIMON + 1 = 1 and Version of: 11-Dec-09 z2 = cos(⇡ /2) + i sin(⇡ /2), so then 103 z2 = cos(103(⇡ /2)) + i sin(103(⇡ /2)) 3⇡ 3⇡ = cos(50⇡ + ) + i sin(50⇡ + ) 2 2 3⇡ 3⇡ = cos( ) + i sin( ) 2 2 = 0 + i( 1) = Or recognize that i2 = 1(i) = i. 1, so i4 = 1. Thus i100 = (i4 )25 = 1, so then i103 = i100 i3 = (1)(i3 ) = i3 = (i2 )i = A2 (d): z3 has absolute value C EDRIC C HAUVE , FALL 2013 i. q 1 2 + 1 2 = 1 and argument ⇡ /4: z3 = cos( ⇡ /4) + i sin( ⇡ /4), 1 f a cu lty of sc ie nce d ep ar tment of mathem atics Week Date 1 Sept 7 I.1, I.2, I.3 2 14 I.4, I.5, I.6 3 21 II.1, II.2, II.3 4 28 II.4, II.5, II.6 5 Oct 5 III.1, III.2 6 12 IV.1, IV.2 7 19 IV.3, IV.4 8 26 9 Nov 2 so then Sections from FS2009 IV.5 V.1 9 VI.1 12 ⇡ A.3/ C i 2 23 IX.3 25 IX.4 13 30 Dec 10 10 Topic/Sections MATH 232 A SSIGNMENT #6 Notes/Speaker Combinatorial Structures FS: Part A.1, A.2 Comtet74 Handout #1 (self study) Symbolic methods Handout #1 (self-study) Asymptotic methods ⇡ i 2 Introduction to Prob. Mariolys FS: Part C (rotating presentations) Combinatorial instances of discrete Mariolys Continuous Limit Laws Marni Quasi-Powers and Gaussian limit laws Sophie 29 z3 Unlabelled structures/4)) + i sin(29( ⇡ /4)) = cos(29( ⇡ 5⇡ 5⇡ Labelled structures I = cos( 6⇡ ) + i sin( 6⇡ ) 4 Labelled structures II 4 5⇡ 5⇡ Combinatorial Combinatorial =...
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