Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-6+6i)+(-9+4i)= -6+6i -9+4i =\color{red}{-6-9}\color{blue}{+6i +4i}=\color{red}{-15}\color{blue}{+10i}\)
2. \((-7+3i) \cdot (-7-7i)= 49+49i -21 i-21i^2 = 49+49i -21 i+21= \color{red}{49+21}\color{blue}{+49i -21i}=\color{red}{70}\color{blue}{+28i}\)
3. \((-1-6i)\cdot (-9i)= +9 i+54i^2 = \color{red}{-54}\color{blue}{+9i}\)
4. \(\frac{3+9i}{10+2i}= \frac{3+9i}{10+2i} \cdot \frac{10-2i}{10-2i} = \frac{30-6i +90 i-18i^2 }{(10)^2-(2i)^2} = \frac{30-6i +90 i+18}{100 + 4} = \frac{48+84i }{104} = \frac{6}{13} - \frac{-21}{26}i \)
5. \((-8+9i)+(4-7i)= -8+9i +4-7i =\color{red}{-8+4}\color{blue}{+9i -7i}=\color{red}{-4}\color{blue}{+2i}\)
6. \(\frac{-6-2i}{10-10i}= \frac{-6-2i}{10-10i} \cdot \frac{10+10i}{10+10i} = \frac{-60-60i -20 i-20i^2 }{(10)^2-(-10i)^2} = \frac{-60-60i -20 i+20}{100 + 100} = \frac{-40-80i }{200} = \frac{-1}{5} + \frac{-2}{5}i \)
7. \((-2-4i) \cdot (-10+6i)= 20-12i +40 i-24i^2 = 20-12i +40 i+24= \color{red}{20+24}\color{blue}{-12i +40i}=\color{red}{44}\color{blue}{+28i}\)
8. \((5-2i)\cdot (-i)= -5 i+2i^2 = \color{red}{-2}\color{blue}{-5i}\)
9. \((-5+10i)-(-5-5i)= -5+10i +5+5i =\color{red}{-5+5}\color{blue}{+10i +5i}=\color{blue}{15i}\)
10. \((8+6i)-(10-8i)= 8+6i -10+8i =\color{red}{8-10}\color{blue}{+6i +8i}=\color{red}{-2}\color{blue}{+14i}\)
11. \((+6i) \cdot (9+10i)= +54 i+60i^2 = \color{red}{-60}\color{blue}{+54i}\)
12. \((-2i) \cdot (10-7i)= -20 i+14i^2 = \color{red}{-14}\color{blue}{-20i}\)