Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((8+i)\cdot (+i)= +8 i+i^2 = \color{red}{-1}\color{blue}{+8i}\)
2. \((-7+6i) \cdot (-5-6i)= 35+42i -30 i-36i^2 = 35+42i -30 i+36= \color{red}{35+36}\color{blue}{+42i -30i}=\color{red}{71}\color{blue}{+12i}\)
3. \((-5+10i)-(-7-10i)= -5+10i +7+10i =\color{red}{-5+7}\color{blue}{+10i +10i}=\color{red}{2}\color{blue}{+20i}\)
4. \(\frac{7+3i}{8+9i}= \frac{7+3i}{8+9i} \cdot \frac{8-9i}{8-9i} = \frac{56-63i +24 i-27i^2 }{(8)^2-(9i)^2} = \frac{56-63i +24 i+27}{64 + 81} = \frac{83-39i }{145} = \frac{83}{145} + \frac{-39}{145}i \)
5. \((6-9i)\cdot (+3i)= +18 i-27i^2 = \color{red}{27}\color{blue}{+18i}\)
6. \((2-2i)+(-3+9i)= 2-2i -3+9i =\color{red}{2-3}\color{blue}{-2i +9i}=\color{red}{-1}\color{blue}{+7i}\)
7. \((7+2i)-(-9-6i)= 7+2i +9+6i =\color{red}{7+9}\color{blue}{+2i +6i}=\color{red}{16}\color{blue}{+8i}\)
8. \(\frac{-4-4i}{-4+6i}= \frac{-4-4i}{-4+6i} \cdot \frac{-4-6i}{-4-6i} = \frac{16+24i +16 i+24i^2 }{(-4)^2-(6i)^2} = \frac{16+24i +16 i-24}{16 + 36} = \frac{-8+40i }{52} = \frac{-2}{13} - \frac{-10}{13}i \)
9. \((-7-2i)-(-2-2i)= -7-2i +2+2i =\color{red}{-7+2}\color{blue}{-2i +2i}=\color{red}{-5}\)
10. \((4+7i)-(9+i)= 4+7i -9-i =\color{red}{4-9}\color{blue}{+7i -i}=\color{red}{-5}\color{blue}{+6i}\)
11. \((-6+7i) \cdot (-6+i)= 36-6i -42 i+7i^2 = 36-6i -42 i-7= \color{red}{36-7}\color{blue}{-6i -42i}=\color{red}{29}\color{blue}{-48i}\)
12. \((-2-2i)+(3+4i)= -2-2i +3+4i =\color{red}{-2+3}\color{blue}{-2i +4i}=\color{red}{1}\color{blue}{+2i}\)