Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4-9i)+(-7-6i)= -4-9i -7-6i =\color{red}{-4-7}\color{blue}{-9i -6i}=\color{red}{-11}\color{blue}{-15i}\)
2. \((+3i) \cdot (9-6i)= +27 i-18i^2 = \color{red}{18}\color{blue}{+27i}\)
3. \((8-3i) \cdot (4+5i)= 32+40i -12 i-15i^2 = 32+40i -12 i+15= \color{red}{32+15}\color{blue}{+40i -12i}=\color{red}{47}\color{blue}{+28i}\)
4. \(\frac{6+i}{6+7i}= \frac{6+i}{6+7i} \cdot \frac{6-7i}{6-7i} = \frac{36-42i +6 i-7i^2 }{(6)^2-(7i)^2} = \frac{36-42i +6 i+7}{36 + 49} = \frac{43-36i }{85} = \frac{43}{85} + \frac{-36}{85}i \)
5. \((-10+i)-(-7+7i)= -10+i +7-7i =\color{red}{-10+7}\color{blue}{+i -7i}=\color{red}{-3}\color{blue}{-6i}\)
6. \((-3+4i)-(-3+7i)= -3+4i +3-7i =\color{red}{-3+3}\color{blue}{+4i -7i}=\color{blue}{-3i}\)
7. \((-7i) \cdot (-7+8i)= +49 i-56i^2 = \color{red}{56}\color{blue}{+49i}\)
8. \((5+7i)-(8-2i)= 5+7i -8+2i =\color{red}{5-8}\color{blue}{+7i +2i}=\color{red}{-3}\color{blue}{+9i}\)
9. \((7+6i)-(-8+i)= 7+6i +8-i =\color{red}{7+8}\color{blue}{+6i -i}=\color{red}{15}\color{blue}{+5i}\)
10. \(\frac{-6+5i}{-3+6i}= \frac{-6+5i}{-3+6i} \cdot \frac{-3-6i}{-3-6i} = \frac{18+36i -15 i-30i^2 }{(-3)^2-(6i)^2} = \frac{18+36i -15 i+30}{9 + 36} = \frac{48+21i }{45} = \frac{16}{15} - \frac{-7}{15}i \)
11. \((3-8i) \cdot (2-7i)= 6-21i -16 i+56i^2 = 6-21i -16 i-56= \color{red}{6-56}\color{blue}{-21i -16i}=\color{red}{-50}\color{blue}{-37i}\)
12. \((9-4i)+(6-3i)= 9-4i +6-3i =\color{red}{9+6}\color{blue}{-4i -3i}=\color{red}{15}\color{blue}{-7i}\)