Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-7-i}{4+9i}= \frac{-7-i}{4+9i} \cdot \frac{4-9i}{4-9i} = \frac{-28+63i -4 i+9i^2 }{(4)^2-(9i)^2} = \frac{-28+63i -4 i-9}{16 + 81} = \frac{-37+59i }{97} = \frac{-37}{97} - \frac{-59}{97}i \)
2. \((-8-7i)+(4-3i)= -8-7i +4-3i =\color{red}{-8+4}\color{blue}{-7i -3i}=\color{red}{-4}\color{blue}{-10i}\)
3. \((-1-3i) \cdot (3+5i)= -3-5i -9 i-15i^2 = -3-5i -9 i+15= \color{red}{-3+15}\color{blue}{-5i -9i}=\color{red}{12}\color{blue}{-14i}\)
4. \((8+5i) \cdot (2-2i)= 16-16i +10 i-10i^2 = 16-16i +10 i+10= \color{red}{16+10}\color{blue}{-16i +10i}=\color{red}{26}\color{blue}{-6i}\)
5. \((-10-10i)-(10-5i)= -10-10i -10+5i =\color{red}{-10-10}\color{blue}{-10i +5i}=\color{red}{-20}\color{blue}{-5i}\)
6. \(\frac{5-8i}{-7-3i}= \frac{5-8i}{-7-3i} \cdot \frac{-7+3i}{-7+3i} = \frac{-35+15i +56 i-24i^2 }{(-7)^2-(-3i)^2} = \frac{-35+15i +56 i+24}{49 + 9} = \frac{-11+71i }{58} = \frac{-11}{58} - \frac{-71}{58}i \)
7. \((-2-7i)+(2+4i)= -2-7i +2+4i =\color{red}{-2+2}\color{blue}{-7i +4i}=\color{blue}{-3i}\)
8. \((-2-10i)-(4-6i)= -2-10i -4+6i =\color{red}{-2-4}\color{blue}{-10i +6i}=\color{red}{-6}\color{blue}{-4i}\)
9. \((-5+i)-(6+6i)= -5+i -6-6i =\color{red}{-5-6}\color{blue}{+i -6i}=\color{red}{-11}\color{blue}{-5i}\)
10. \((5+9i)\cdot (+10i)= +50 i+90i^2 = \color{red}{-90}\color{blue}{+50i}\)
11. \((-3-9i)+(-2-3i)= -3-9i -2-3i =\color{red}{-3-2}\color{blue}{-9i -3i}=\color{red}{-5}\color{blue}{-12i}\)
12. \(\frac{-1-5i}{-9-4i}= \frac{-1-5i}{-9-4i} \cdot \frac{-9+4i}{-9+4i} = \frac{9-4i +45 i-20i^2 }{(-9)^2-(-4i)^2} = \frac{9-4i +45 i+20}{81 + 16} = \frac{29+41i }{97} = \frac{29}{97} - \frac{-41}{97}i \)