Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8i) \cdot (4+i)= -32 i-8i^2 = \color{red}{8}\color{blue}{-32i}\)
2. \((-4i) \cdot (1+i)= -4 i-4i^2 = \color{red}{4}\color{blue}{-4i}\)
3. \((9-9i) \cdot (7+5i)= 63+45i -63 i-45i^2 = 63+45i -63 i+45= \color{red}{63+45}\color{blue}{+45i -63i}=\color{red}{108}\color{blue}{-18i}\)
4. \((-5+i)+(9-9i)= -5+i +9-9i =\color{red}{-5+9}\color{blue}{+i -9i}=\color{red}{4}\color{blue}{-8i}\)
5. \((-3+2i) \cdot (1+2i)= -3-6i +2 i+4i^2 = -3-6i +2 i-4= \color{red}{-3-4}\color{blue}{-6i +2i}=\color{red}{-7}\color{blue}{-4i}\)
6. \(\frac{-5+2i}{8-i}= \frac{-5+2i}{8-i} \cdot \frac{8+i}{8+i} = \frac{-40-5i +16 i+2i^2 }{(8)^2-(-1i)^2} = \frac{-40-5i +16 i-2}{64 + 1} = \frac{-42+11i }{65} = \frac{-42}{65} - \frac{-11}{65}i \)
7. \((4+3i) \cdot (4-9i)= 16-36i +12 i-27i^2 = 16-36i +12 i+27= \color{red}{16+27}\color{blue}{-36i +12i}=\color{red}{43}\color{blue}{-24i}\)
8. \((-5-4i)\cdot (+i)= -5 i-4i^2 = \color{red}{4}\color{blue}{-5i}\)
9. \((-3-9i)-(-3-8i)= -3-9i +3+8i =\color{red}{-3+3}\color{blue}{-9i +8i}=\color{blue}{-i}\)
10. \((-8+8i)+(-3-5i)= -8+8i -3-5i =\color{red}{-8-3}\color{blue}{+8i -5i}=\color{red}{-11}\color{blue}{+3i}\)
11. \((9+3i) \cdot (-3-10i)= -27-90i -9 i-30i^2 = -27-90i -9 i+30= \color{red}{-27+30}\color{blue}{-90i -9i}=\color{red}{3}\color{blue}{-99i}\)
12. \((-2+7i)-(-6-2i)= -2+7i +6+2i =\color{red}{-2+6}\color{blue}{+7i +2i}=\color{red}{4}\color{blue}{+9i}\)