Vermenigvuldigen en delen (a+bi)

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Bereken

1. \((-9-6i) \cdot (6+8i)\)
2. \((-6+7i) \cdot (-10-9i)\)
3. \((+3i) \cdot (-7+i)\)
4. \((-3-8i) \cdot (-5+3i)\)
5. \(\frac{5+6i}{-3-2i}\)
6. \((-3-10i)\cdot (+6i)\)
7. \((-9+9i)\cdot (-8i)\)
8. \((8-9i) \cdot (2+3i)\)
9. \(\frac{-8+9i}{3-8i}\)
10. \(\frac{-1+5i}{-5-10i}\)
11. \((-4i) \cdot (8+i)\)
12. \((-7-i) \cdot (-7-6i)\)

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Bereken

Verbetersleutel

1. \((-9-6i) \cdot (6+8i)= -54-72i -36 i-48i^2 = -54-72i -36 i+48= \color{red}{-54+48}\color{blue}{-72i -36i}=\color{red}{-6}\color{blue}{-108i}\)
2. \((-6+7i) \cdot (-10-9i)= 60+54i -70 i-63i^2 = 60+54i -70 i+63= \color{red}{60+63}\color{blue}{+54i -70i}=\color{red}{123}\color{blue}{-16i}\)
3. \((+3i) \cdot (-7+i)= -21 i+3i^2 = \color{red}{-3}\color{blue}{-21i}\)
4. \((-3-8i) \cdot (-5+3i)= 15-9i +40 i-24i^2 = 15-9i +40 i+24= \color{red}{15+24}\color{blue}{-9i +40i}=\color{red}{39}\color{blue}{+31i}\)
5. \(\frac{5+6i}{-3-2i}= \frac{5+6i}{-3-2i} \cdot \frac{-3+2i}{-3+2i} = \frac{-15+10i -18 i+12i^2 }{(-3)^2-(-2i)^2} = \frac{-15+10i -18 i-12}{9 + 4} = \frac{-27-8i }{13} = \frac{-27}{13} + \frac{-8}{13}i \)
6. \((-3-10i)\cdot (+6i)= -18 i-60i^2 = \color{red}{60}\color{blue}{-18i}\)
7. \((-9+9i)\cdot (-8i)= +72 i-72i^2 = \color{red}{72}\color{blue}{+72i}\)
8. \((8-9i) \cdot (2+3i)= 16+24i -18 i-27i^2 = 16+24i -18 i+27= \color{red}{16+27}\color{blue}{+24i -18i}=\color{red}{43}\color{blue}{+6i}\)
9. \(\frac{-8+9i}{3-8i}= \frac{-8+9i}{3-8i} \cdot \frac{3+8i}{3+8i} = \frac{-24-64i +27 i+72i^2 }{(3)^2-(-8i)^2} = \frac{-24-64i +27 i-72}{9 + 64} = \frac{-96-37i }{73} = \frac{-96}{73} + \frac{-37}{73}i \)
10. \(\frac{-1+5i}{-5-10i}= \frac{-1+5i}{-5-10i} \cdot \frac{-5+10i}{-5+10i} = \frac{5-10i -25 i+50i^2 }{(-5)^2-(-10i)^2} = \frac{5-10i -25 i-50}{25 + 100} = \frac{-45-35i }{125} = \frac{-9}{25} + \frac{-7}{25}i \)
11. \((-4i) \cdot (8+i)= -32 i-4i^2 = \color{red}{4}\color{blue}{-32i}\)
12. \((-7-i) \cdot (-7-6i)= 49+42i +7 i+6i^2 = 49+42i +7 i-6= \color{red}{49-6}\color{blue}{+42i +7i}=\color{red}{43}\color{blue}{+49i}\)