Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4-7i)\cdot (+10i)= -40 i-70i^2 = \color{red}{70}\color{blue}{-40i}\)
2. \((-6+4i)-(1+4i)= -6+4i -1-4i =\color{red}{-6-1}\color{blue}{+4i -4i}=\color{red}{-7}\)
3. \((4+3i) \cdot (-2+3i)= -8+12i -6 i+9i^2 = -8+12i -6 i-9= \color{red}{-8-9}\color{blue}{+12i -6i}=\color{red}{-17}\color{blue}{+6i}\)
4. \((-3-4i)+(1-8i)= -3-4i +1-8i =\color{red}{-3+1}\color{blue}{-4i -8i}=\color{red}{-2}\color{blue}{-12i}\)
5. \((-4+3i)+(7+i)= -4+3i +7+i =\color{red}{-4+7}\color{blue}{+3i +i}=\color{red}{3}\color{blue}{+4i}\)
6. \((-1-6i) \cdot (-4+9i)= 4-9i +24 i-54i^2 = 4-9i +24 i+54= \color{red}{4+54}\color{blue}{-9i +24i}=\color{red}{58}\color{blue}{+15i}\)
7. \((-4+2i)\cdot (-8i)= +32 i-16i^2 = \color{red}{16}\color{blue}{+32i}\)
8. \((2-8i)-(9-8i)= 2-8i -9+8i =\color{red}{2-9}\color{blue}{-8i +8i}=\color{red}{-7}\)
9. \(\frac{2-3i}{2-2i}= \frac{2-3i}{2-2i} \cdot \frac{2+2i}{2+2i} = \frac{4+4i -6 i-6i^2 }{(2)^2-(-2i)^2} = \frac{4+4i -6 i+6}{4 + 4} = \frac{10-2i }{8} = \frac{5}{4} + \frac{-1}{4}i \)
10. \((-6-5i)\cdot (-6i)= +36 i+30i^2 = \color{red}{-30}\color{blue}{+36i}\)
11. \((-8-9i)\cdot (-4i)= +32 i+36i^2 = \color{red}{-36}\color{blue}{+32i}\)
12. \((1-9i)\cdot (+6i)= +6 i-54i^2 = \color{red}{54}\color{blue}{+6i}\)