Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((6-2i) \cdot (-3-3i)= -18-18i +6 i+6i^2 = -18-18i +6 i-6= \color{red}{-18-6}\color{blue}{-18i +6i}=\color{red}{-24}\color{blue}{-12i}\)
2. \(\frac{-5+8i}{3-6i}= \frac{-5+8i}{3-6i} \cdot \frac{3+6i}{3+6i} = \frac{-15-30i +24 i+48i^2 }{(3)^2-(-6i)^2} = \frac{-15-30i +24 i-48}{9 + 36} = \frac{-63-6i }{45} = \frac{-7}{5} + \frac{-2}{15}i \)
3. \((-8-3i)-(1+10i)= -8-3i -1-10i =\color{red}{-8-1}\color{blue}{-3i -10i}=\color{red}{-9}\color{blue}{-13i}\)
4. \((-2i) \cdot (-7+4i)= +14 i-8i^2 = \color{red}{8}\color{blue}{+14i}\)
5. \((1-4i)+(-8-6i)= 1-4i -8-6i =\color{red}{1-8}\color{blue}{-4i -6i}=\color{red}{-7}\color{blue}{-10i}\)
6. \((6-5i)+(2-8i)= 6-5i +2-8i =\color{red}{6+2}\color{blue}{-5i -8i}=\color{red}{8}\color{blue}{-13i}\)
7. \((8+7i)-(3-5i)= 8+7i -3+5i =\color{red}{8-3}\color{blue}{+7i +5i}=\color{red}{5}\color{blue}{+12i}\)
8. \((10-6i) \cdot (3-7i)= 30-70i -18 i+42i^2 = 30-70i -18 i-42= \color{red}{30-42}\color{blue}{-70i -18i}=\color{red}{-12}\color{blue}{-88i}\)
9. \((2+3i) \cdot (-10-4i)= -20-8i -30 i-12i^2 = -20-8i -30 i+12= \color{red}{-20+12}\color{blue}{-8i -30i}=\color{red}{-8}\color{blue}{-38i}\)
10. \((-7+10i)-(1+8i)= -7+10i -1-8i =\color{red}{-7-1}\color{blue}{+10i -8i}=\color{red}{-8}\color{blue}{+2i}\)
11. \((1+2i)+(4+6i)= 1+2i +4+6i =\color{red}{1+4}\color{blue}{+2i +6i}=\color{red}{5}\color{blue}{+8i}\)
12. \((7+5i) \cdot (10+3i)= 70+21i +50 i+15i^2 = 70+21i +50 i-15= \color{red}{70-15}\color{blue}{+21i +50i}=\color{red}{55}\color{blue}{+71i}\)