Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+9i)-(5-8i)= -4+9i -5+8i =\color{red}{-4-5}\color{blue}{+9i +8i}=\color{red}{-9}\color{blue}{+17i}\)
2. \((-6-i) \cdot (10+5i)= -60-30i -10 i-5i^2 = -60-30i -10 i+5= \color{red}{-60+5}\color{blue}{-30i -10i}=\color{red}{-55}\color{blue}{-40i}\)
3. \((-4-10i)+(4-4i)= -4-10i +4-4i =\color{red}{-4+4}\color{blue}{-10i -4i}=\color{blue}{-14i}\)
4. \((10-2i) \cdot (-5+2i)= -50+20i +10 i-4i^2 = -50+20i +10 i+4= \color{red}{-50+4}\color{blue}{+20i +10i}=\color{red}{-46}\color{blue}{+30i}\)
5. \((7-7i)+(6-i)= 7-7i +6-i =\color{red}{7+6}\color{blue}{-7i -i}=\color{red}{13}\color{blue}{-8i}\)
6. \((3+10i) \cdot (-3-4i)= -9-12i -30 i-40i^2 = -9-12i -30 i+40= \color{red}{-9+40}\color{blue}{-12i -30i}=\color{red}{31}\color{blue}{-42i}\)
7. \((-10-8i)+(1+7i)= -10-8i +1+7i =\color{red}{-10+1}\color{blue}{-8i +7i}=\color{red}{-9}\color{blue}{-i}\)
8. \((2-2i)-(-10+5i)= 2-2i +10-5i =\color{red}{2+10}\color{blue}{-2i -5i}=\color{red}{12}\color{blue}{-7i}\)
9. \(\frac{-3+5i}{5-8i}= \frac{-3+5i}{5-8i} \cdot \frac{5+8i}{5+8i} = \frac{-15-24i +25 i+40i^2 }{(5)^2-(-8i)^2} = \frac{-15-24i +25 i-40}{25 + 64} = \frac{-55+i }{89} = \frac{-55}{89} - \frac{-1}{89}i \)
10. \(\frac{-8+9i}{3+10i}= \frac{-8+9i}{3+10i} \cdot \frac{3-10i}{3-10i} = \frac{-24+80i +27 i-90i^2 }{(3)^2-(10i)^2} = \frac{-24+80i +27 i+90}{9 + 100} = \frac{66+107i }{109} = \frac{66}{109} - \frac{-107}{109}i \)
11. \((-9-i)\cdot (+9i)= -81 i-9i^2 = \color{red}{9}\color{blue}{-81i}\)
12. \((4+i)\cdot (-4i)= -16 i-4i^2 = \color{red}{4}\color{blue}{-16i}\)