Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((8-4i)\cdot (-3i)= -24 i+12i^2 = \color{red}{-12}\color{blue}{-24i}\)
2. \((+3i) \cdot (1-10i)= +3 i-30i^2 = \color{red}{30}\color{blue}{+3i}\)
3. \((-7-10i) \cdot (-4-8i)= 28+56i +40 i+80i^2 = 28+56i +40 i-80= \color{red}{28-80}\color{blue}{+56i +40i}=\color{red}{-52}\color{blue}{+96i}\)
4. \(\frac{-2-2i}{-6+2i}= \frac{-2-2i}{-6+2i} \cdot \frac{-6-2i}{-6-2i} = \frac{12+4i +12 i+4i^2 }{(-6)^2-(2i)^2} = \frac{12+4i +12 i-4}{36 + 4} = \frac{8+16i }{40} = \frac{1}{5} - \frac{-2}{5}i \)
5. \((2+3i) \cdot (-7-i)= -14-2i -21 i-3i^2 = -14-2i -21 i+3= \color{red}{-14+3}\color{blue}{-2i -21i}=\color{red}{-11}\color{blue}{-23i}\)
6. \(\frac{2+2i}{3+9i}= \frac{2+2i}{3+9i} \cdot \frac{3-9i}{3-9i} = \frac{6-18i +6 i-18i^2 }{(3)^2-(9i)^2} = \frac{6-18i +6 i+18}{9 + 81} = \frac{24-12i }{90} = \frac{4}{15} + \frac{-2}{15}i \)
7. \(\frac{-10-10i}{9-5i}= \frac{-10-10i}{9-5i} \cdot \frac{9+5i}{9+5i} = \frac{-90-50i -90 i-50i^2 }{(9)^2-(-5i)^2} = \frac{-90-50i -90 i+50}{81 + 25} = \frac{-40-140i }{106} = \frac{-20}{53} + \frac{-70}{53}i \)
8. \((-4+9i) \cdot (4-8i)= -16+32i +36 i-72i^2 = -16+32i +36 i+72= \color{red}{-16+72}\color{blue}{+32i +36i}=\color{red}{56}\color{blue}{+68i}\)
9. \((-9i) \cdot (-9+9i)= +81 i-81i^2 = \color{red}{81}\color{blue}{+81i}\)
10. \((-9-10i)\cdot (+4i)= -36 i-40i^2 = \color{red}{40}\color{blue}{-36i}\)
11. \((-7-4i) \cdot (-5+5i)= 35-35i +20 i-20i^2 = 35-35i +20 i+20= \color{red}{35+20}\color{blue}{-35i +20i}=\color{red}{55}\color{blue}{-15i}\)
12. \((-9-2i)\cdot (+8i)= -72 i-16i^2 = \color{red}{16}\color{blue}{-72i}\)