College Algebra & Trigonometry, 2018a

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1.4. COMPLEX NUMBERS 41 Expressing square roots of negative numbers Square roots of negative quantities are generally expressed as a multiple of i. Examples √ −4=2i. √ −25 = 5i √ −7 ≈ 2.646i Adding, subtracting and multiplying with complex numbers Calculating with complex numbers has many similarities to working with variables. The real part and imginary part are treated separately for addition and subtraction, but can be multiplied and divided. Examples Compute the following: (6 − 4i)+(−2+7i) =4+3i (−9+2i) − (−4+6i) =−9+2i +4− 6i = −5 − 4i 3(10 + i) =30+3i −7i(−5+8i) =35i − 56i 2 Now we encounter an interesting fact about complex numbers and, in particular, the complex unit i. By definition, i = √ −1. Therefore, if we square i we should get −1. In the last example problem above, we can replace the i 2 with −1 to finish the problem.
42 CHAPTER 1. ALGEBRA REVIEW −7i(−5+8i) =35i − 56i 2 =35i − 56(−1) =35i +56 =56+35i Examples Compute the following: (8 − 5i)(1 − 4i) =8− 32i − 5i +20i 2 =8− 37i + 20(−1) =8− 37i − 20 = −12 − 37i (9+2i) 2 =(9+2i)(9+2i) =81+18i +18i +4i 2 =81+36i +4(−1) =81+36i − 4 =77+36i
Page 1 and 2: College Algebra & Trigonometry
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92 CHAPTER 2. POLYNOMIAL AND RATION
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100 CHAPTER 2. POLYNOMIAL AND RATIO
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190 CHAPTER 4. FUNCTIONS by substit
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192 CHAPTER 4. FUNCTIONS 4.2 Domain
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194 CHAPTER 4. FUNCTIONS Exercises
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196 CHAPTER 4. FUNCTIONS 8) 12 10 8
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198 CHAPTER 4. FUNCTIONS We can use
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200 CHAPTER 4. FUNCTIONS 3) 20 16 1
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202 CHAPTER 4. FUNCTIONS Vertical S
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214 CHAPTER 4. FUNCTIONS 3) Match e
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218 CHAPTER 4. FUNCTIONS Being fami
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222 CHAPTER 4. FUNCTIONS 4.6 Piecew
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242 CHAPTER 4. FUNCTIONS 8) A recta
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248 CHAPTER 4. FUNCTIONS Distance O
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250 CHAPTER 4. FUNCTIONS The graph
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258 CHAPTER 5. CONIC SECTIONS - CIR
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288 CHAPTER 6. SEQUENCES AND SERIES
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438 CHAPTER 10. TRIGONOMETRIC IDENT
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472 CHAPTER 11. THE LAW OF SINES TH
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College Algebra & Trigonometry, 2018a

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