Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9-i)-(-10-10i)= 9-i +10+10i =\color{red}{9+10}\color{blue}{-i +10i}=\color{red}{19}\color{blue}{+9i}\)
2. \(\frac{6+5i}{-4+8i}= \frac{6+5i}{-4+8i} \cdot \frac{-4-8i}{-4-8i} = \frac{-24-48i -20 i-40i^2 }{(-4)^2-(8i)^2} = \frac{-24-48i -20 i+40}{16 + 64} = \frac{16-68i }{80} = \frac{1}{5} + \frac{-17}{20}i \)
3. \((1-8i)-(-5+3i)= 1-8i +5-3i =\color{red}{1+5}\color{blue}{-8i -3i}=\color{red}{6}\color{blue}{-11i}\)
4. \((-7-2i) \cdot (3-3i)= -21+21i -6 i+6i^2 = -21+21i -6 i-6= \color{red}{-21-6}\color{blue}{+21i -6i}=\color{red}{-27}\color{blue}{+15i}\)
5. \((7+4i) \cdot (5-6i)= 35-42i +20 i-24i^2 = 35-42i +20 i+24= \color{red}{35+24}\color{blue}{-42i +20i}=\color{red}{59}\color{blue}{-22i}\)
6. \((1-2i) \cdot (-5-3i)= -5-3i +10 i+6i^2 = -5-3i +10 i-6= \color{red}{-5-6}\color{blue}{-3i +10i}=\color{red}{-11}\color{blue}{+7i}\)
7. \((-5+2i)\cdot (+8i)= -40 i+16i^2 = \color{red}{-16}\color{blue}{-40i}\)
8. \((4-6i)+(2+8i)= 4-6i +2+8i =\color{red}{4+2}\color{blue}{-6i +8i}=\color{red}{6}\color{blue}{+2i}\)
9. \((-3i) \cdot (5-8i)= -15 i+24i^2 = \color{red}{-24}\color{blue}{-15i}\)
10. \((-2-4i) \cdot (6-3i)= -12+6i -24 i+12i^2 = -12+6i -24 i-12= \color{red}{-12-12}\color{blue}{+6i -24i}=\color{red}{-24}\color{blue}{-18i}\)
11. \((7-5i)-(-6-8i)= 7-5i +6+8i =\color{red}{7+6}\color{blue}{-5i +8i}=\color{red}{13}\color{blue}{+3i}\)
12. \((-10+6i)+(-6+3i)= -10+6i -6+3i =\color{red}{-10-6}\color{blue}{+6i +3i}=\color{red}{-16}\color{blue}{+9i}\)