Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{4+3i}{-10-3i}= \frac{4+3i}{-10-3i} \cdot \frac{-10+3i}{-10+3i} = \frac{-40+12i -30 i+9i^2 }{(-10)^2-(-3i)^2} = \frac{-40+12i -30 i-9}{100 + 9} = \frac{-49-18i }{109} = \frac{-49}{109} + \frac{-18}{109}i \)
2. \((8-i)+(-2-9i)= 8-i -2-9i =\color{red}{8-2}\color{blue}{-i -9i}=\color{red}{6}\color{blue}{-10i}\)
3. \(\frac{-1-9i}{-3-7i}= \frac{-1-9i}{-3-7i} \cdot \frac{-3+7i}{-3+7i} = \frac{3-7i +27 i-63i^2 }{(-3)^2-(-7i)^2} = \frac{3-7i +27 i+63}{9 + 49} = \frac{66+20i }{58} = \frac{33}{29} - \frac{-10}{29}i \)
4. \(\frac{6+7i}{-5-i}= \frac{6+7i}{-5-i} \cdot \frac{-5+i}{-5+i} = \frac{-30+6i -35 i+7i^2 }{(-5)^2-(-1i)^2} = \frac{-30+6i -35 i-7}{25 + 1} = \frac{-37-29i }{26} = \frac{-37}{26} + \frac{-29}{26}i \)
5. \((-6-8i)-(4+9i)= -6-8i -4-9i =\color{red}{-6-4}\color{blue}{-8i -9i}=\color{red}{-10}\color{blue}{-17i}\)
6. \((1+6i)+(-10-5i)= 1+6i -10-5i =\color{red}{1-10}\color{blue}{+6i -5i}=\color{red}{-9}\color{blue}{+i}\)
7. \((3+7i)-(10+7i)= 3+7i -10-7i =\color{red}{3-10}\color{blue}{+7i -7i}=\color{red}{-7}\)
8. \((-10+5i)+(-7-8i)= -10+5i -7-8i =\color{red}{-10-7}\color{blue}{+5i -8i}=\color{red}{-17}\color{blue}{-3i}\)
9. \((9-8i)-(-2-5i)= 9-8i +2+5i =\color{red}{9+2}\color{blue}{-8i +5i}=\color{red}{11}\color{blue}{-3i}\)
10. \((-6i) \cdot (3+10i)= -18 i-60i^2 = \color{red}{60}\color{blue}{-18i}\)
11. \((-3+8i) \cdot (4-3i)= -12+9i +32 i-24i^2 = -12+9i +32 i+24= \color{red}{-12+24}\color{blue}{+9i +32i}=\color{red}{12}\color{blue}{+41i}\)
12. \((6+10i) \cdot (6+8i)= 36+48i +60 i+80i^2 = 36+48i +60 i-80= \color{red}{36-80}\color{blue}{+48i +60i}=\color{red}{-44}\color{blue}{+108i}\)