Section%201.5

Section%201.5 - /' FW fetjifiexfl MA 180 - Precalculus _....

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Unformatted text preview: /' FW fetjifiexfl MA 180 - Precalculus _. - - Professor Terry . Section 1.5 Complex Numbers E Complex Numbers and Operations with Complex Numbers @412 M awake/r5 TR Type of numbers required ~ 1M are 1 were u e 3 X .. Irra/trtwdfl ampere x =4 C was H28 « Complex number a+bi , where a and b are real ’-{-*th' ‘3 , numbers and i2 = -l 61 4 5t 31 L Imaginary number a+bi with bee. Pure imaginary number In“ with b :0 Definition: Sum (a +bi) +(c+a’i) = (a + c) + (b + d)i Write the expression in the form a+bi . where a and b are real numbers. (—5+7i)+(4+9i) Z (—E—HA -—+ (Tweefld "2 l—ifl-HLMr k Definition: Difference (a + bi) — (c+ ch") = (a — c) + (b n d)i Write the expression in the form a+bi , where a and b are real numbers. (—3+8i)—(2+3i) 1’ 65+ 3L) + (‘9‘ 5t.) a G 3 ‘ 3 “tr g‘E'DL “‘ — S 75.2% Definition: Product ((1 + bi)(c + di) = ac + adz' + bci + bar:2 = (ac $217+ (ad + bc)i Write the expression in the form a+bi , where a and b are real numbers. ‘ ’Z (6+7i)2 =(®+7¢)(O+763 ‘2 30+‘(QLI‘H‘3C’f‘ Halli—J", ‘ 2 30 aqu +<3L4L z l-—¢3+E‘(¢(L «wee—3r) 2 '6G—eeirj went—oi Z a. 6o+o ~10; ifafloei 1'92 z (L'H>2320323 1m MA‘iBO Sect .5 SpringO4 ewt Definition: Multiplication by a real number k k(a +bz‘) =ka +(kb)z‘ 7) ‘ Write the expression in the form a+bi , where a and b are real numbers. @)_(7_30 a QLi-t-UC *‘H-Bc’ ‘2 (ll/{573+ (0+3),- ‘f(2—7i)2 ‘2 z _+L{,C(L'2) ' at L—d5“1%tl)z rl—tgb “ZS/(:1— : 495433 1‘— (Q‘K "(l9ka Definition: Equality a + bi = c + di if and only if a = c and b = d Find the values of x and y, where x and y are real numbers. (x—y)+3i = 7+yi Em? POW/“L X “ “cl z7j\> X :C i... fl __ Mung SE 537 Wald... GO_5>+3L.:7+3L: ‘52 '0 7+2); =q+e¢ / We can now solve x2 = —4 X 2 2M? i a J Con'u ates and Quotients of Com lex Numbers Definition of the Con'u ate of a Com lex Number: if z = a +bi is a complex number, then its conjugate, denoted by z, is a—bi. 3i. Properties of Coniugates __ _ (2—7i)+(82+‘ie) ‘2: @+33 ’i (‘q‘r‘f7L3 "2 +091 2 (2—7f)(a‘fhll:) '2 Li "tMW/“Lm (“El 2 i" ‘°EC"(“‘3 2 4+qu The sum and product of a Complex number and its conjugate are (‘gg ‘ numbers. MA180 Sec1.5 SpringO4 ewt l l Write the expression in the forn@~here a and b are real numbers. ‘ .5 __ 5” a Qflb. 2 75(él't'lcfv z IO-lv‘fb‘SLr 2—71' 1 3-7.; 811'“: {DWEXEM'IQ ‘53 lTb “afiirf Write the expression in the forhere a and b are real numbers. '— 3" Jo) 5 "QLFB —3—2i 5+21‘ m: 2 {:37 = 5o Multiply: 5475‘ 2' (iv/é— : 5C: 1 z 2 @ Note: If only one'of a or b is negative, then JEJE=JE. F=J¥i =Lxfl: Write the expression in the form a +bi , where a and b are real numbers. ewflfimflfifi z (~3+SC)(?'G£> Multiply: Definition: Principle square root «f—r for r > O . t1 2 *M won warez—30:, 2- wq + Sm“ —BO(Hr\ -l 30 MA180 8901.5 SpringO4 ewt \ Eguations with Comglex Solutions ' Find the Solution of the Equation: 1:2 —2x+26: 0 at! X: “('23 i Quiz-LNNZO Me) _ _2 Of i } C 2 X z a i V H "' ‘0 L" . I a X x3~27= dais—b5 w (a—bDCéLQ —e d/(O + to“) Find the Solution of the Equation: x 1(5): (x ~3 UCXD’ +3J( + ‘1 320 X-BEO Q3 XZ—th—M no Jitgb “baa (ML/3Q {2&0ng X2 *3: TAHOE!) 5.10) X ,2 — =5 :t W a) __ x 2 —~ 3 i W ' "mi: ##11‘5 i 3 L MA180 Sec1.5 Springo4 ewt ...
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Section%201.5 - /' FW fetjifiexfl MA 180 - Precalculus _....

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