Online notes for Math 15, Math for Liberal Arts taught in the Fall 2016 semester at Laney College by Prof. Hubbard.
a] (4 + i) + (7 - i)Answer: 11b] (4 + i) - (7 - i)Answer: -3 + 2ic] (7 - i) - (4 + i)Answer: 3 - 2id] (4 + i) * (7 - i)FOIL: 28 - 4i + 7i - i^2 = 28 - 4i + 7i + 1 = Answer: 29 + 3ie] (4 + i) / (7 - i)Multiply by (7 + i)/(7 + i)Numerator FOIL = 28 + 4i + 7i + i^2 = 28 + 4i + 7i - 1 = 27 + 11iDenominator FOIL = 49 + 7i - 7i - i^2 = 49 + 7i - 7i + 1=50Answer: 27/50 + 11i/50f] (7 - i) / (4 + i)Multiply by (4 - i)/(4 - i)Numerator FOIL = 28 - 7i - 4i + i^2 = 28 - 7i - 4i - 1 = 27 - 11iDenominator FOIL = 16 - 4i + 4i - i^2 = 16 + 7i - 7i + 1=17Answer: 27/17 - 11i/17
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a] (4 + i) + (7 - i)
Answer: 11
b] (4 + i) - (7 - i)
Answer: -3 + 2i
c] (7 - i) - (4 + i)
Answer: 3 - 2i
d] (4 + i) * (7 - i)
FOIL: 28 - 4i + 7i - i^2 =
28 - 4i + 7i + 1 =
Answer: 29 + 3i
e] (4 + i) / (7 - i)
Multiply by (7 + i)/(7 + i)
Numerator FOIL = 28 + 4i + 7i + i^2 =
28 + 4i + 7i - 1 =
27 + 11i
Denominator FOIL =
49 + 7i - 7i - i^2 =
49 + 7i - 7i + 1=
50
Answer: 27/50 + 11i/50
f] (7 - i) / (4 + i)
Multiply by (4 - i)/(4 - i)
Numerator FOIL = 28 - 7i - 4i + i^2 =
28 - 7i - 4i - 1 =
27 - 11i
Denominator FOIL =
16 - 4i + 4i - i^2 =
16 + 7i - 7i + 1=
17
Answer: 27/17 - 11i/17
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