Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3-8i) \cdot (-7+3i)= 21-9i +56 i-24i^2 = 21-9i +56 i+24= \color{red}{21+24}\color{blue}{-9i +56i}=\color{red}{45}\color{blue}{+47i}\)
2. \(\frac{-1+2i}{-6+3i}= \frac{-1+2i}{-6+3i} \cdot \frac{-6-3i}{-6-3i} = \frac{6+3i -12 i-6i^2 }{(-6)^2-(3i)^2} = \frac{6+3i -12 i+6}{36 + 9} = \frac{12-9i }{45} = \frac{4}{15} + \frac{-1}{5}i \)
3. \(\frac{-3-6i}{-1-7i}= \frac{-3-6i}{-1-7i} \cdot \frac{-1+7i}{-1+7i} = \frac{3-21i +6 i-42i^2 }{(-1)^2-(-7i)^2} = \frac{3-21i +6 i+42}{1 + 49} = \frac{45-15i }{50} = \frac{9}{10} + \frac{-3}{10}i \)
4. \((3-3i)\cdot (+8i)= +24 i-24i^2 = \color{red}{24}\color{blue}{+24i}\)
5. \((-6+9i) \cdot (6-3i)= -36+18i +54 i-27i^2 = -36+18i +54 i+27= \color{red}{-36+27}\color{blue}{+18i +54i}=\color{red}{-9}\color{blue}{+72i}\)
6. \(\frac{-8-i}{-1+9i}= \frac{-8-i}{-1+9i} \cdot \frac{-1-9i}{-1-9i} = \frac{8+72i +1 i+9i^2 }{(-1)^2-(9i)^2} = \frac{8+72i +1 i-9}{1 + 81} = \frac{-1+73i }{82} = \frac{-1}{82} - \frac{-73}{82}i \)
7. \((+3i) \cdot (-2-3i)= -6 i-9i^2 = \color{red}{9}\color{blue}{-6i}\)
8. \((7-10i)-(6-9i)= 7-10i -6+9i =\color{red}{7-6}\color{blue}{-10i +9i}=\color{red}{1}\color{blue}{-i}\)
9. \((-1+9i) \cdot (-7+10i)= 7-10i -63 i+90i^2 = 7-10i -63 i-90= \color{red}{7-90}\color{blue}{-10i -63i}=\color{red}{-83}\color{blue}{-73i}\)
10. \((-4+4i) \cdot (4+5i)= -16-20i +16 i+20i^2 = -16-20i +16 i-20= \color{red}{-16-20}\color{blue}{-20i +16i}=\color{red}{-36}\color{blue}{-4i}\)
11. \((6+4i)+(-6+i)= 6+4i -6+i =\color{red}{6-6}\color{blue}{+4i +i}=\color{blue}{5i}\)
12. \((3+10i)+(2-8i)= 3+10i +2-8i =\color{red}{3+2}\color{blue}{+10i -8i}=\color{red}{5}\color{blue}{+2i}\)