Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+3i) \cdot (1+10i)= +3 i+30i^2 = \color{red}{-30}\color{blue}{+3i}\)
2. \(\frac{-8-10i}{10+8i}= \frac{-8-10i}{10+8i} \cdot \frac{10-8i}{10-8i} = \frac{-80+64i -100 i+80i^2 }{(10)^2-(8i)^2} = \frac{-80+64i -100 i-80}{100 + 64} = \frac{-160-36i }{164} = \frac{-40}{41} + \frac{-9}{41}i \)
3. \((1-10i)-(-10+8i)= 1-10i +10-8i =\color{red}{1+10}\color{blue}{-10i -8i}=\color{red}{11}\color{blue}{-18i}\)
4. \((-4-8i)-(8+8i)= -4-8i -8-8i =\color{red}{-4-8}\color{blue}{-8i -8i}=\color{red}{-12}\color{blue}{-16i}\)
5. \((5+3i) \cdot (-3+5i)= -15+25i -9 i+15i^2 = -15+25i -9 i-15= \color{red}{-15-15}\color{blue}{+25i -9i}=\color{red}{-30}\color{blue}{+16i}\)
6. \((-7-3i)\cdot (+4i)= -28 i-12i^2 = \color{red}{12}\color{blue}{-28i}\)
7. \((1+2i)\cdot (-6i)= -6 i-12i^2 = \color{red}{12}\color{blue}{-6i}\)
8. \((3+i) \cdot (1-6i)= 3-18i +1 i-6i^2 = 3-18i +1 i+6= \color{red}{3+6}\color{blue}{-18i +i}=\color{red}{9}\color{blue}{-17i}\)
9. \(\frac{5+5i}{9+5i}= \frac{5+5i}{9+5i} \cdot \frac{9-5i}{9-5i} = \frac{45-25i +45 i-25i^2 }{(9)^2-(5i)^2} = \frac{45-25i +45 i+25}{81 + 25} = \frac{70+20i }{106} = \frac{35}{53} - \frac{-10}{53}i \)
10. \((-10i) \cdot (-6-8i)= +60 i+80i^2 = \color{red}{-80}\color{blue}{+60i}\)
11. \((6+5i)-(-4-7i)= 6+5i +4+7i =\color{red}{6+4}\color{blue}{+5i +7i}=\color{red}{10}\color{blue}{+12i}\)
12. \((-7-10i)-(5-6i)= -7-10i -5+6i =\color{red}{-7-5}\color{blue}{-10i +6i}=\color{red}{-12}\color{blue}{-4i}\)