Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9-5i)+(10+4i)= 9-5i +10+4i =\color{red}{9+10}\color{blue}{-5i +4i}=\color{red}{19}\color{blue}{-i}\)
2. \((-7-4i)+(-6-2i)= -7-4i -6-2i =\color{red}{-7-6}\color{blue}{-4i -2i}=\color{red}{-13}\color{blue}{-6i}\)
3. \((-10-10i)\cdot (-i)= +10 i+10i^2 = \color{red}{-10}\color{blue}{+10i}\)
4. \((5+3i)+(-4+7i)= 5+3i -4+7i =\color{red}{5-4}\color{blue}{+3i +7i}=\color{red}{1}\color{blue}{+10i}\)
5. \((2-6i)-(-9-10i)= 2-6i +9+10i =\color{red}{2+9}\color{blue}{-6i +10i}=\color{red}{11}\color{blue}{+4i}\)
6. \((5-10i) \cdot (1+i)= 5+5i -10 i-10i^2 = 5+5i -10 i+10= \color{red}{5+10}\color{blue}{+5i -10i}=\color{red}{15}\color{blue}{-5i}\)
7. \(\frac{-6+6i}{3-8i}= \frac{-6+6i}{3-8i} \cdot \frac{3+8i}{3+8i} = \frac{-18-48i +18 i+48i^2 }{(3)^2-(-8i)^2} = \frac{-18-48i +18 i-48}{9 + 64} = \frac{-66-30i }{73} = \frac{-66}{73} + \frac{-30}{73}i \)
8. \(\frac{3-i}{-6-4i}= \frac{3-i}{-6-4i} \cdot \frac{-6+4i}{-6+4i} = \frac{-18+12i +6 i-4i^2 }{(-6)^2-(-4i)^2} = \frac{-18+12i +6 i+4}{36 + 16} = \frac{-14+18i }{52} = \frac{-7}{26} - \frac{-9}{26}i \)
9. \((-2-5i)+(-3+7i)= -2-5i -3+7i =\color{red}{-2-3}\color{blue}{-5i +7i}=\color{red}{-5}\color{blue}{+2i}\)
10. \((-3+2i) \cdot (-5-4i)= 15+12i -10 i-8i^2 = 15+12i -10 i+8= \color{red}{15+8}\color{blue}{+12i -10i}=\color{red}{23}\color{blue}{+2i}\)
11. \((-6-4i) \cdot (1-5i)= -6+30i -4 i+20i^2 = -6+30i -4 i-20= \color{red}{-6-20}\color{blue}{+30i -4i}=\color{red}{-26}\color{blue}{+26i}\)
12. \((-10+7i)\cdot (-9i)= +90 i-63i^2 = \color{red}{63}\color{blue}{+90i}\)