Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1-i)-(5+2i)= -1-i -5-2i =\color{red}{-1-5}\color{blue}{-i -2i}=\color{red}{-6}\color{blue}{-3i}\)
2. \((-i) \cdot (3+8i)= -3 i-8i^2 = \color{red}{8}\color{blue}{-3i}\)
3. \((1-9i) \cdot (7-3i)= 7-3i -63 i+27i^2 = 7-3i -63 i-27= \color{red}{7-27}\color{blue}{-3i -63i}=\color{red}{-20}\color{blue}{-66i}\)
4. \(\frac{6+3i}{6-6i}= \frac{6+3i}{6-6i} \cdot \frac{6+6i}{6+6i} = \frac{36+36i +18 i+18i^2 }{(6)^2-(-6i)^2} = \frac{36+36i +18 i-18}{36 + 36} = \frac{18+54i }{72} = \frac{1}{4} - \frac{-3}{4}i \)
5. \(\frac{-3-8i}{4-8i}= \frac{-3-8i}{4-8i} \cdot \frac{4+8i}{4+8i} = \frac{-12-24i -32 i-64i^2 }{(4)^2-(-8i)^2} = \frac{-12-24i -32 i+64}{16 + 64} = \frac{52-56i }{80} = \frac{13}{20} + \frac{-7}{10}i \)
6. \((7+3i)+(6-10i)= 7+3i +6-10i =\color{red}{7+6}\color{blue}{+3i -10i}=\color{red}{13}\color{blue}{-7i}\)
7. \(\frac{9+6i}{9-9i}= \frac{9+6i}{9-9i} \cdot \frac{9+9i}{9+9i} = \frac{81+81i +54 i+54i^2 }{(9)^2-(-9i)^2} = \frac{81+81i +54 i-54}{81 + 81} = \frac{27+135i }{162} = \frac{1}{6} - \frac{-5}{6}i \)
8. \((-5+i) \cdot (-8-10i)= 40+50i -8 i-10i^2 = 40+50i -8 i+10= \color{red}{40+10}\color{blue}{+50i -8i}=\color{red}{50}\color{blue}{+42i}\)
9. \((9-6i)+(-7-4i)= 9-6i -7-4i =\color{red}{9-7}\color{blue}{-6i -4i}=\color{red}{2}\color{blue}{-10i}\)
10. \((-8-4i)+(2-4i)= -8-4i +2-4i =\color{red}{-8+2}\color{blue}{-4i -4i}=\color{red}{-6}\color{blue}{-8i}\)
11. \((7-9i)-(-4-6i)= 7-9i +4+6i =\color{red}{7+4}\color{blue}{-9i +6i}=\color{red}{11}\color{blue}{-3i}\)
12. \((+10i) \cdot (-1-5i)= -10 i-50i^2 = \color{red}{50}\color{blue}{-10i}\)