Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((2-3i)+(3+8i)= 2-3i +3+8i =\color{red}{2+3}\color{blue}{-3i +8i}=\color{red}{5}\color{blue}{+5i}\)
2. \((3-3i)\cdot (-10i)= -30 i+30i^2 = \color{red}{-30}\color{blue}{-30i}\)
3. \((-7-5i)+(-3+7i)= -7-5i -3+7i =\color{red}{-7-3}\color{blue}{-5i +7i}=\color{red}{-10}\color{blue}{+2i}\)
4. \((-7+5i)-(-6+3i)= -7+5i +6-3i =\color{red}{-7+6}\color{blue}{+5i -3i}=\color{red}{-1}\color{blue}{+2i}\)
5. \((-5-2i)-(-1+i)= -5-2i +1-i =\color{red}{-5+1}\color{blue}{-2i -i}=\color{red}{-4}\color{blue}{-3i}\)
6. \((3+6i)+(-7+9i)= 3+6i -7+9i =\color{red}{3-7}\color{blue}{+6i +9i}=\color{red}{-4}\color{blue}{+15i}\)
7. \((-5-9i) \cdot (-9+i)= 45-5i +81 i-9i^2 = 45-5i +81 i+9= \color{red}{45+9}\color{blue}{-5i +81i}=\color{red}{54}\color{blue}{+76i}\)
8. \((10-3i) \cdot (-8-7i)= -80-70i +24 i+21i^2 = -80-70i +24 i-21= \color{red}{-80-21}\color{blue}{-70i +24i}=\color{red}{-101}\color{blue}{-46i}\)
9. \((5+i)\cdot (+5i)= +25 i+5i^2 = \color{red}{-5}\color{blue}{+25i}\)
10. \((-5+9i)-(-10-7i)= -5+9i +10+7i =\color{red}{-5+10}\color{blue}{+9i +7i}=\color{red}{5}\color{blue}{+16i}\)
11. \(\frac{7+7i}{-2+10i}= \frac{7+7i}{-2+10i} \cdot \frac{-2-10i}{-2-10i} = \frac{-14-70i -14 i-70i^2 }{(-2)^2-(10i)^2} = \frac{-14-70i -14 i+70}{4 + 100} = \frac{56-84i }{104} = \frac{7}{13} + \frac{-21}{26}i \)
12. \((-10-5i) \cdot (-6-8i)= 60+80i +30 i+40i^2 = 60+80i +30 i-40= \color{red}{60-40}\color{blue}{+80i +30i}=\color{red}{20}\color{blue}{+110i}\)