Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((1-8i)+(-6-9i)= 1-8i -6-9i =\color{red}{1-6}\color{blue}{-8i -9i}=\color{red}{-5}\color{blue}{-17i}\)
2. \((4-5i)+(-7+9i)= 4-5i -7+9i =\color{red}{4-7}\color{blue}{-5i +9i}=\color{red}{-3}\color{blue}{+4i}\)
3. \((-2-8i) \cdot (10+3i)= -20-6i -80 i-24i^2 = -20-6i -80 i+24= \color{red}{-20+24}\color{blue}{-6i -80i}=\color{red}{4}\color{blue}{-86i}\)
4. \((-8-2i)+(6+3i)= -8-2i +6+3i =\color{red}{-8+6}\color{blue}{-2i +3i}=\color{red}{-2}\color{blue}{+i}\)
5. \((2-3i)-(1-4i)= 2-3i -1+4i =\color{red}{2-1}\color{blue}{-3i +4i}=\color{red}{1}\color{blue}{+i}\)
6. \((1+4i)+(2-5i)= 1+4i +2-5i =\color{red}{1+2}\color{blue}{+4i -5i}=\color{red}{3}\color{blue}{-i}\)
7. \((-6+4i)+(6-9i)= -6+4i +6-9i =\color{red}{-6+6}\color{blue}{+4i -9i}=\color{blue}{-5i}\)
8. \((9+5i) \cdot (8-3i)= 72-27i +40 i-15i^2 = 72-27i +40 i+15= \color{red}{72+15}\color{blue}{-27i +40i}=\color{red}{87}\color{blue}{+13i}\)
9. \((4+i)-(-2+6i)= 4+i +2-6i =\color{red}{4+2}\color{blue}{+i -6i}=\color{red}{6}\color{blue}{-5i}\)
10. \((9-4i)-(-5+8i)= 9-4i +5-8i =\color{red}{9+5}\color{blue}{-4i -8i}=\color{red}{14}\color{blue}{-12i}\)
11. \((-6+10i) \cdot (-8-9i)= 48+54i -80 i-90i^2 = 48+54i -80 i+90= \color{red}{48+90}\color{blue}{+54i -80i}=\color{red}{138}\color{blue}{-26i}\)
12. \(\frac{-4-10i}{-4-5i}= \frac{-4-10i}{-4-5i} \cdot \frac{-4+5i}{-4+5i} = \frac{16-20i +40 i-50i^2 }{(-4)^2-(-5i)^2} = \frac{16-20i +40 i+50}{16 + 25} = \frac{66+20i }{41} = \frac{66}{41} - \frac{-20}{41}i \)