Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7-4i)+(8+3i)= -7-4i +8+3i =\color{red}{-7+8}\color{blue}{-4i +3i}=\color{red}{1}\color{blue}{-i}\)
2. \(\frac{1-7i}{-9-9i}= \frac{1-7i}{-9-9i} \cdot \frac{-9+9i}{-9+9i} = \frac{-9+9i +63 i-63i^2 }{(-9)^2-(-9i)^2} = \frac{-9+9i +63 i+63}{81 + 81} = \frac{54+72i }{162} = \frac{1}{3} - \frac{-4}{9}i \)
3. \((-5+9i)\cdot (-7i)= +35 i-63i^2 = \color{red}{63}\color{blue}{+35i}\)
4. \((3-4i) \cdot (6+2i)= 18+6i -24 i-8i^2 = 18+6i -24 i+8= \color{red}{18+8}\color{blue}{+6i -24i}=\color{red}{26}\color{blue}{-18i}\)
5. \((-3-5i)+(-4+4i)= -3-5i -4+4i =\color{red}{-3-4}\color{blue}{-5i +4i}=\color{red}{-7}\color{blue}{-i}\)
6. \((-8-6i)-(-6-3i)= -8-6i +6+3i =\color{red}{-8+6}\color{blue}{-6i +3i}=\color{red}{-2}\color{blue}{-3i}\)
7. \((-6+9i)-(8-3i)= -6+9i -8+3i =\color{red}{-6-8}\color{blue}{+9i +3i}=\color{red}{-14}\color{blue}{+12i}\)
8. \(\frac{-8+9i}{5+5i}= \frac{-8+9i}{5+5i} \cdot \frac{5-5i}{5-5i} = \frac{-40+40i +45 i-45i^2 }{(5)^2-(5i)^2} = \frac{-40+40i +45 i+45}{25 + 25} = \frac{5+85i }{50} = \frac{1}{10} - \frac{-17}{10}i \)
9. \((10+i) \cdot (-4+4i)= -40+40i -4 i+4i^2 = -40+40i -4 i-4= \color{red}{-40-4}\color{blue}{+40i -4i}=\color{red}{-44}\color{blue}{+36i}\)
10. \(\frac{-10+4i}{6-2i}= \frac{-10+4i}{6-2i} \cdot \frac{6+2i}{6+2i} = \frac{-60-20i +24 i+8i^2 }{(6)^2-(-2i)^2} = \frac{-60-20i +24 i-8}{36 + 4} = \frac{-68+4i }{40} = \frac{-17}{10} - \frac{-1}{10}i \)
11. \((-10+9i)-(-10+4i)= -10+9i +10-4i =\color{red}{-10+10}\color{blue}{+9i -4i}=\color{blue}{5i}\)
12. \(\frac{-6+5i}{3-8i}= \frac{-6+5i}{3-8i} \cdot \frac{3+8i}{3+8i} = \frac{-18-48i +15 i+40i^2 }{(3)^2-(-8i)^2} = \frac{-18-48i +15 i-40}{9 + 64} = \frac{-58-33i }{73} = \frac{-58}{73} + \frac{-33}{73}i \)