Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5+9i)\cdot (+9i)= +45 i+81i^2 = \color{red}{-81}\color{blue}{+45i}\)
2. \((2-3i) \cdot (6-4i)= 12-8i -18 i+12i^2 = 12-8i -18 i-12= \color{red}{12-12}\color{blue}{-8i -18i}=\color{blue}{-26i}\)
3. \((3-7i)\cdot (+4i)= +12 i-28i^2 = \color{red}{28}\color{blue}{+12i}\)
4. \((2+2i)\cdot (-i)= -2 i-2i^2 = \color{red}{2}\color{blue}{-2i}\)
5. \((2+6i) \cdot (5+4i)= 10+8i +30 i+24i^2 = 10+8i +30 i-24= \color{red}{10-24}\color{blue}{+8i +30i}=\color{red}{-14}\color{blue}{+38i}\)
6. \((10-3i) \cdot (-2-7i)= -20-70i +6 i+21i^2 = -20-70i +6 i-21= \color{red}{-20-21}\color{blue}{-70i +6i}=\color{red}{-41}\color{blue}{-64i}\)
7. \((2-9i)-(3-i)= 2-9i -3+i =\color{red}{2-3}\color{blue}{-9i +i}=\color{red}{-1}\color{blue}{-8i}\)
8. \((-7i) \cdot (8-9i)= -56 i+63i^2 = \color{red}{-63}\color{blue}{-56i}\)
9. \(\frac{-8-6i}{-2-6i}= \frac{-8-6i}{-2-6i} \cdot \frac{-2+6i}{-2+6i} = \frac{16-48i +12 i-36i^2 }{(-2)^2-(-6i)^2} = \frac{16-48i +12 i+36}{4 + 36} = \frac{52-36i }{40} = \frac{13}{10} + \frac{-9}{10}i \)
10. \((5+2i)-(-9-i)= 5+2i +9+i =\color{red}{5+9}\color{blue}{+2i +i}=\color{red}{14}\color{blue}{+3i}\)
11. \(\frac{2-3i}{-9-6i}= \frac{2-3i}{-9-6i} \cdot \frac{-9+6i}{-9+6i} = \frac{-18+12i +27 i-18i^2 }{(-9)^2-(-6i)^2} = \frac{-18+12i +27 i+18}{81 + 36} = \frac{0+39i }{117} = 0- \frac{-1}{3}i \)
12. \(\frac{10-7i}{2-8i}= \frac{10-7i}{2-8i} \cdot \frac{2+8i}{2+8i} = \frac{20+80i -14 i-56i^2 }{(2)^2-(-8i)^2} = \frac{20+80i -14 i+56}{4 + 64} = \frac{76+66i }{68} = \frac{19}{17} - \frac{-33}{34}i \)