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120_12.7_notes - Definition Mat120f121 Chapter 7 Section 7...

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Unformatted text preview: / Definition: Mat120f121 Chapter 7 - Section 7 P831”) 2 ‘0 THE IMAGINARY UNIT 1 The high-nary Ink iis defined as i: V—l. where 31.: —1. Complex Number: A complex numberisofthe form a +bi where a iscalled theRealPart and hi isealledflielmginaryl’art. How the Complex Number System fits with what we have been working with already. COMPLEX NUMBER SYSTEM REAL NUMBER SYSTEM- A\ 5\ .\\\\\n\ “3 NUMBERSA \\;;\n} \b\‘;\‘,;‘\, \B‘xfi ‘ \\\\\‘\\\\\ i z J__1 non- Munln non- repeatingng decimal. \\m\\\\\\\ mm INTEGERS _ __ _‘ _ ' "' " ' " \erg |\e\.\\\\ _ {-3-2-10123‘...} mJéor 35* '21 13:. , I"'l .- I 3 II _! II I _I .' . .m- ' - . . ' any radical WHOLENdueens - that can't be - . ' - «’"r'" - I“??? simplified iMAGINAFlY NUMBERS 2 I acouunuen :NUMBEns ~- 2\ i i .. to complain the complex number system: {n+bi I a and b are real mailbox, ”to, M0} 'IiiiliililllIIIIIIlemplu: 3+2i, -5+71, 7.2+.031, etc. \’V Mat120/ 121 Chapter 0 - Section 7 Page y Complex Number System 717 In Exercises 1-16, express each number in terms ofi and simplify if possible. 2. 4-36 8. —— J—45 l6. 6 — 11—98 36’ “/ ’“‘ y’ "I '5‘. Adding is just combining "like" terms. 18. (6+5i) + (4+3i) 22. (11+8i) — (2 + Si) 32. @:M% //+$7£~af>’/ —-/ In Exercises 33-62, find each product and write the result in the form a + bi. «Multiply as you would if the i's were variables. 38. —6i(3—5i) «a/S’f +30 Cl“ M/X6-3o (4 + i)(5+6i) so. (5 427 i)(5 + J5 i) 52. (3 + 2i)2 0’10 +§Qt+gqfi4gi 25151193,. . I ‘+,56;1-—3;L » $1,141 Q—é4—291-(a 24/ c @ 51%.: Mat120/121 UV Chapter. - Section 7 In Exercises 63-84, divide and simplify to the form a + bi. Conjugate: Examples: Expression: 441’ “-01 —C Issue with the Conjugate: Conjugate : Page QO’LS) ...
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