Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7-i) \cdot (-2+4i)= 14-28i +2 i-4i^2 = 14-28i +2 i+4= \color{red}{14+4}\color{blue}{-28i +2i}=\color{red}{18}\color{blue}{-26i}\)
2. \(\frac{-9-6i}{-10+2i}= \frac{-9-6i}{-10+2i} \cdot \frac{-10-2i}{-10-2i} = \frac{90+18i +60 i+12i^2 }{(-10)^2-(2i)^2} = \frac{90+18i +60 i-12}{100 + 4} = \frac{78+78i }{104} = \frac{3}{4} - \frac{-3}{4}i \)
3. \((2-4i)-(-2+2i)= 2-4i +2-2i =\color{red}{2+2}\color{blue}{-4i -2i}=\color{red}{4}\color{blue}{-6i}\)
4. \((-3+9i)-(4+6i)= -3+9i -4-6i =\color{red}{-3-4}\color{blue}{+9i -6i}=\color{red}{-7}\color{blue}{+3i}\)
5. \((8+i)\cdot (-9i)= -72 i-9i^2 = \color{red}{9}\color{blue}{-72i}\)
6. \((-9-9i)\cdot (+5i)= -45 i-45i^2 = \color{red}{45}\color{blue}{-45i}\)
7. \((-9-5i) \cdot (-1-9i)= 9+81i +5 i+45i^2 = 9+81i +5 i-45= \color{red}{9-45}\color{blue}{+81i +5i}=\color{red}{-36}\color{blue}{+86i}\)
8. \((10+9i) \cdot (2+5i)= 20+50i +18 i+45i^2 = 20+50i +18 i-45= \color{red}{20-45}\color{blue}{+50i +18i}=\color{red}{-25}\color{blue}{+68i}\)
9. \((-7+i) \cdot (-2-6i)= 14+42i -2 i-6i^2 = 14+42i -2 i+6= \color{red}{14+6}\color{blue}{+42i -2i}=\color{red}{20}\color{blue}{+40i}\)
10. \((1+5i)+(-8+4i)= 1+5i -8+4i =\color{red}{1-8}\color{blue}{+5i +4i}=\color{red}{-7}\color{blue}{+9i}\)
11. \((8-7i) \cdot (-7-7i)= -56-56i +49 i+49i^2 = -56-56i +49 i-49= \color{red}{-56-49}\color{blue}{-56i +49i}=\color{red}{-105}\color{blue}{-7i}\)
12. \((8+9i)+(-10+4i)= 8+9i -10+4i =\color{red}{8-10}\color{blue}{+9i +4i}=\color{red}{-2}\color{blue}{+13i}\)