Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3-i)+(-9-6i)= -3-i -9-6i =\color{red}{-3-9}\color{blue}{-i -6i}=\color{red}{-12}\color{blue}{-7i}\)
2. \(\frac{10-10i}{-6+8i}= \frac{10-10i}{-6+8i} \cdot \frac{-6-8i}{-6-8i} = \frac{-60-80i +60 i+80i^2 }{(-6)^2-(8i)^2} = \frac{-60-80i +60 i-80}{36 + 64} = \frac{-140-20i }{100} = \frac{-7}{5} + \frac{-1}{5}i \)
3. \(\frac{10-5i}{-10+3i}= \frac{10-5i}{-10+3i} \cdot \frac{-10-3i}{-10-3i} = \frac{-100-30i +50 i+15i^2 }{(-10)^2-(3i)^2} = \frac{-100-30i +50 i-15}{100 + 9} = \frac{-115+20i }{109} = \frac{-115}{109} - \frac{-20}{109}i \)
4. \((+8i) \cdot (9+8i)= +72 i+64i^2 = \color{red}{-64}\color{blue}{+72i}\)
5. \((3-i)+(-3+9i)= 3-i -3+9i =\color{red}{3-3}\color{blue}{-i +9i}=\color{blue}{8i}\)
6. \((10+2i)-(10+8i)= 10+2i -10-8i =\color{red}{10-10}\color{blue}{+2i -8i}=\color{blue}{-6i}\)
7. \((-7+5i) \cdot (3-10i)= -21+70i +15 i-50i^2 = -21+70i +15 i+50= \color{red}{-21+50}\color{blue}{+70i +15i}=\color{red}{29}\color{blue}{+85i}\)
8. \((2-2i)-(2+3i)= 2-2i -2-3i =\color{red}{2-2}\color{blue}{-2i -3i}=\color{blue}{-5i}\)
9. \((1+6i)+(-10+6i)= 1+6i -10+6i =\color{red}{1-10}\color{blue}{+6i +6i}=\color{red}{-9}\color{blue}{+12i}\)
10. \((-9-4i)\cdot (+9i)= -81 i-36i^2 = \color{red}{36}\color{blue}{-81i}\)
11. \((8+4i)+(7+2i)= 8+4i +7+2i =\color{red}{8+7}\color{blue}{+4i +2i}=\color{red}{15}\color{blue}{+6i}\)
12. \((2+2i)-(-6-3i)= 2+2i +6+3i =\color{red}{2+6}\color{blue}{+2i +3i}=\color{red}{8}\color{blue}{+5i}\)