Lecture 4 Notes

Number 1 a bic di a bi c di complex number

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Unformatted text preview: c + di) = a + c + (b + d)i Complex number review • Adding two complex numbers: (a + bi) + (c + di) = a + c + (b + d)i Complex number review • Adding two complex numbers: (a + bi) + (c + di) = a + c + (b + d)i • Multiplying two complex numbers: (a + bi)(c + di) = ac − bd + (ad + bc)i Complex number review • Adding two complex numbers: (a + bi) + (c + di) = a + c + (b + d)i • Multiplying two complex numbers: (a + bi)(c + di) = ac − bd + (ad + bc)i Complex number review • Adding two complex numbers: (a + bi) + (c + di) = a + c + (b + d)i • Multiplying two complex numbers: (a + bi)(c + di) = ac − bd + (ad + bc)i Complex number review • Adding two complex numbers: (a + bi) + (c + di) = a + c + (b + d)i • Multiplying two complex numbers: (a + bi)(c + di) = ac − bd + (ad + bc)i • Dividing by a complex number: 1 (a + bi)/(c + di) = (a + bi) (c + di) Complex number review • Adding two complex numbers: (a + bi) + (c + di) = a + c + (b + d)i • Multiplying two complex numbers: (a + bi)(c + di) = ac − bd + (ad + bc)i • Dividing by a complex number: 1 (a + bi)/(c + di) = (a + bi) (c + di) • What is the inverse of c+di? Complex number review • What is the inverse of c+di? (A) c − di (C) (B) c + di c2 + d2 (D) • Dividing by a complex number: c − di c2 + d2 1 c − di Complex number review • What is the inverse of c+di? (A) c − di (C) (B) c + di c2 + d2 (D) c − di c2 + d2 1 c − di c − di c + d − (cd − dc)i (c + di) 2 = =1 2 2 + d2 c +d c 2 • Dividing by a complex number: 2 Complex number review • What is the inverse of c+di? (A) c − di (C) (B) c + di c2 + d2 (D) c − di c2 + d2 1 c − di c − di c + d − (cd − dc)i (c + di) 2 = =1 2 2 + d2 c +d c 2 • Dividing by a complex number: 2 Complex number review • What is the inverse of c+di? (A) c − di (C) (B) c + di c2 + d2 (D) c − di c2 + d2 1 c − di c − di c + d − (cd − dc)i (c + di) 2 = =1 2 2 + d2 c +d c 2 • Dividing by a complex number: 2 Complex number review • What is the inverse of c+di? (A) c − di (C) (B) c + di c2 + d2 (D) c − di c2 + d2 1 c − di c − di c + d − (cd − dc)i (c + di) 2 = =1 2 2 + d2 c +d c 2 • Dividing by a complex number: (a + bi)/(c + di...
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