Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-4-i}{6-9i}= \frac{-4-i}{6-9i} \cdot \frac{6+9i}{6+9i} = \frac{-24-36i -6 i-9i^2 }{(6)^2-(-9i)^2} = \frac{-24-36i -6 i+9}{36 + 81} = \frac{-15-42i }{117} = \frac{-5}{39} + \frac{-14}{39}i \)
2. \((-8-5i) \cdot (-9+2i)= 72-16i +45 i-10i^2 = 72-16i +45 i+10= \color{red}{72+10}\color{blue}{-16i +45i}=\color{red}{82}\color{blue}{+29i}\)
3. \((3+2i)-(-6+i)= 3+2i +6-i =\color{red}{3+6}\color{blue}{+2i -i}=\color{red}{9}\color{blue}{+i}\)
4. \((-10+i)+(-6+10i)= -10+i -6+10i =\color{red}{-10-6}\color{blue}{+i +10i}=\color{red}{-16}\color{blue}{+11i}\)
5. \((-2-9i)+(4+6i)= -2-9i +4+6i =\color{red}{-2+4}\color{blue}{-9i +6i}=\color{red}{2}\color{blue}{-3i}\)
6. \((7-10i)-(1+9i)= 7-10i -1-9i =\color{red}{7-1}\color{blue}{-10i -9i}=\color{red}{6}\color{blue}{-19i}\)
7. \(\frac{1+5i}{-10-7i}= \frac{1+5i}{-10-7i} \cdot \frac{-10+7i}{-10+7i} = \frac{-10+7i -50 i+35i^2 }{(-10)^2-(-7i)^2} = \frac{-10+7i -50 i-35}{100 + 49} = \frac{-45-43i }{149} = \frac{-45}{149} + \frac{-43}{149}i \)
8. \((-2+6i)+(-4+3i)= -2+6i -4+3i =\color{red}{-2-4}\color{blue}{+6i +3i}=\color{red}{-6}\color{blue}{+9i}\)
9. \((-4-6i) \cdot (-9+6i)= 36-24i +54 i-36i^2 = 36-24i +54 i+36= \color{red}{36+36}\color{blue}{-24i +54i}=\color{red}{72}\color{blue}{+30i}\)
10. \(\frac{-9-3i}{3+5i}= \frac{-9-3i}{3+5i} \cdot \frac{3-5i}{3-5i} = \frac{-27+45i -9 i+15i^2 }{(3)^2-(5i)^2} = \frac{-27+45i -9 i-15}{9 + 25} = \frac{-42+36i }{34} = \frac{-21}{17} - \frac{-18}{17}i \)
11. \((-1+8i)-(-7+5i)= -1+8i +7-5i =\color{red}{-1+7}\color{blue}{+8i -5i}=\color{red}{6}\color{blue}{+3i}\)
12. \((7+9i)\cdot (+3i)= +21 i+27i^2 = \color{red}{-27}\color{blue}{+21i}\)