Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-9-8i}{1-4i}= \frac{-9-8i}{1-4i} \cdot \frac{1+4i}{1+4i} = \frac{-9-36i -8 i-32i^2 }{(1)^2-(-4i)^2} = \frac{-9-36i -8 i+32}{1 + 16} = \frac{23-44i }{17} = \frac{23}{17} + \frac{-44}{17}i \)
2. \((9-7i)+(-8-6i)= 9-7i -8-6i =\color{red}{9-8}\color{blue}{-7i -6i}=\color{red}{1}\color{blue}{-13i}\)
3. \(\frac{-1+5i}{5-8i}= \frac{-1+5i}{5-8i} \cdot \frac{5+8i}{5+8i} = \frac{-5-8i +25 i+40i^2 }{(5)^2-(-8i)^2} = \frac{-5-8i +25 i-40}{25 + 64} = \frac{-45+17i }{89} = \frac{-45}{89} - \frac{-17}{89}i \)
4. \((2+3i) \cdot (5+6i)= 10+12i +15 i+18i^2 = 10+12i +15 i-18= \color{red}{10-18}\color{blue}{+12i +15i}=\color{red}{-8}\color{blue}{+27i}\)
5. \((-10+4i)\cdot (-i)= +10 i-4i^2 = \color{red}{4}\color{blue}{+10i}\)
6. \(\frac{4+10i}{9+10i}= \frac{4+10i}{9+10i} \cdot \frac{9-10i}{9-10i} = \frac{36-40i +90 i-100i^2 }{(9)^2-(10i)^2} = \frac{36-40i +90 i+100}{81 + 100} = \frac{136+50i }{181} = \frac{136}{181} - \frac{-50}{181}i \)
7. \((-2-3i)+(9+3i)= -2-3i +9+3i =\color{red}{-2+9}\color{blue}{-3i +3i}=\color{red}{7}\)
8. \(\frac{7+8i}{5+3i}= \frac{7+8i}{5+3i} \cdot \frac{5-3i}{5-3i} = \frac{35-21i +40 i-24i^2 }{(5)^2-(3i)^2} = \frac{35-21i +40 i+24}{25 + 9} = \frac{59+19i }{34} = \frac{59}{34} - \frac{-19}{34}i \)
9. \((-5-4i) \cdot (10-6i)= -50+30i -40 i+24i^2 = -50+30i -40 i-24= \color{red}{-50-24}\color{blue}{+30i -40i}=\color{red}{-74}\color{blue}{-10i}\)
10. \(\frac{-4+8i}{3+3i}= \frac{-4+8i}{3+3i} \cdot \frac{3-3i}{3-3i} = \frac{-12+12i +24 i-24i^2 }{(3)^2-(3i)^2} = \frac{-12+12i +24 i+24}{9 + 9} = \frac{12+36i }{18} = \frac{2}{3} - -2i\)
11. \((2+9i)\cdot (+10i)= +20 i+90i^2 = \color{red}{-90}\color{blue}{+20i}\)
12. \((-7-4i) \cdot (4-10i)= -28+70i -16 i+40i^2 = -28+70i -16 i-40= \color{red}{-28-40}\color{blue}{+70i -16i}=\color{red}{-68}\color{blue}{+54i}\)