Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3+3i) \cdot (10+8i)= -30-24i +30 i+24i^2 = -30-24i +30 i-24= \color{red}{-30-24}\color{blue}{-24i +30i}=\color{red}{-54}\color{blue}{+6i}\)
2. \((4+6i)+(-7+4i)= 4+6i -7+4i =\color{red}{4-7}\color{blue}{+6i +4i}=\color{red}{-3}\color{blue}{+10i}\)
3. \((4-4i) \cdot (8-3i)= 32-12i -32 i+12i^2 = 32-12i -32 i-12= \color{red}{32-12}\color{blue}{-12i -32i}=\color{red}{20}\color{blue}{-44i}\)
4. \(\frac{-7+3i}{-5-4i}= \frac{-7+3i}{-5-4i} \cdot \frac{-5+4i}{-5+4i} = \frac{35-28i -15 i+12i^2 }{(-5)^2-(-4i)^2} = \frac{35-28i -15 i-12}{25 + 16} = \frac{23-43i }{41} = \frac{23}{41} + \frac{-43}{41}i \)
5. \(\frac{-8+4i}{6-9i}= \frac{-8+4i}{6-9i} \cdot \frac{6+9i}{6+9i} = \frac{-48-72i +24 i+36i^2 }{(6)^2-(-9i)^2} = \frac{-48-72i +24 i-36}{36 + 81} = \frac{-84-48i }{117} = \frac{-28}{39} + \frac{-16}{39}i \)
6. \((5+i)-(-10-5i)= 5+i +10+5i =\color{red}{5+10}\color{blue}{+i +5i}=\color{red}{15}\color{blue}{+6i}\)
7. \((-i) \cdot (-4-i)= +4 i+i^2 = \color{red}{-1}\color{blue}{+4i}\)
8. \((+8i) \cdot (7+3i)= +56 i+24i^2 = \color{red}{-24}\color{blue}{+56i}\)
9. \((-4-i)-(-9-4i)= -4-i +9+4i =\color{red}{-4+9}\color{blue}{-i +4i}=\color{red}{5}\color{blue}{+3i}\)
10. \((7+5i)+(-10+5i)= 7+5i -10+5i =\color{red}{7-10}\color{blue}{+5i +5i}=\color{red}{-3}\color{blue}{+10i}\)
11. \((1-3i)-(-10+9i)= 1-3i +10-9i =\color{red}{1+10}\color{blue}{-3i -9i}=\color{red}{11}\color{blue}{-12i}\)
12. \((-4-4i)+(7+6i)= -4-4i +7+6i =\color{red}{-4+7}\color{blue}{-4i +6i}=\color{red}{3}\color{blue}{+2i}\)