Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9-3i)-(7+9i)= -9-3i -7-9i =\color{red}{-9-7}\color{blue}{-3i -9i}=\color{red}{-16}\color{blue}{-12i}\)
2. \((-1+9i)+(7-3i)= -1+9i +7-3i =\color{red}{-1+7}\color{blue}{+9i -3i}=\color{red}{6}\color{blue}{+6i}\)
3. \(\frac{-1+2i}{4+9i}= \frac{-1+2i}{4+9i} \cdot \frac{4-9i}{4-9i} = \frac{-4+9i +8 i-18i^2 }{(4)^2-(9i)^2} = \frac{-4+9i +8 i+18}{16 + 81} = \frac{14+17i }{97} = \frac{14}{97} - \frac{-17}{97}i \)
4. \((-6+4i)+(-1-9i)= -6+4i -1-9i =\color{red}{-6-1}\color{blue}{+4i -9i}=\color{red}{-7}\color{blue}{-5i}\)
5. \((-2+i)\cdot (+10i)= -20 i+10i^2 = \color{red}{-10}\color{blue}{-20i}\)
6. \(\frac{5-2i}{6-5i}= \frac{5-2i}{6-5i} \cdot \frac{6+5i}{6+5i} = \frac{30+25i -12 i-10i^2 }{(6)^2-(-5i)^2} = \frac{30+25i -12 i+10}{36 + 25} = \frac{40+13i }{61} = \frac{40}{61} - \frac{-13}{61}i \)
7. \((-10+2i)+(1+8i)= -10+2i +1+8i =\color{red}{-10+1}\color{blue}{+2i +8i}=\color{red}{-9}\color{blue}{+10i}\)
8. \(\frac{-1-10i}{4+9i}= \frac{-1-10i}{4+9i} \cdot \frac{4-9i}{4-9i} = \frac{-4+9i -40 i+90i^2 }{(4)^2-(9i)^2} = \frac{-4+9i -40 i-90}{16 + 81} = \frac{-94-31i }{97} = \frac{-94}{97} + \frac{-31}{97}i \)
9. \((10+4i)-(-3-10i)= 10+4i +3+10i =\color{red}{10+3}\color{blue}{+4i +10i}=\color{red}{13}\color{blue}{+14i}\)
10. \((-2+7i)+(8-3i)= -2+7i +8-3i =\color{red}{-2+8}\color{blue}{+7i -3i}=\color{red}{6}\color{blue}{+4i}\)
11. \((-2-6i)-(3+7i)= -2-6i -3-7i =\color{red}{-2-3}\color{blue}{-6i -7i}=\color{red}{-5}\color{blue}{-13i}\)
12. \(\frac{5-4i}{-4-9i}= \frac{5-4i}{-4-9i} \cdot \frac{-4+9i}{-4+9i} = \frac{-20+45i +16 i-36i^2 }{(-4)^2-(-9i)^2} = \frac{-20+45i +16 i+36}{16 + 81} = \frac{16+61i }{97} = \frac{16}{97} - \frac{-61}{97}i \)