Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-2+6i}{-8+5i}= \frac{-2+6i}{-8+5i} \cdot \frac{-8-5i}{-8-5i} = \frac{16+10i -48 i-30i^2 }{(-8)^2-(5i)^2} = \frac{16+10i -48 i+30}{64 + 25} = \frac{46-38i }{89} = \frac{46}{89} + \frac{-38}{89}i \)
2. \(\frac{4-i}{-9-6i}= \frac{4-i}{-9-6i} \cdot \frac{-9+6i}{-9+6i} = \frac{-36+24i +9 i-6i^2 }{(-9)^2-(-6i)^2} = \frac{-36+24i +9 i+6}{81 + 36} = \frac{-30+33i }{117} = \frac{-10}{39} - \frac{-11}{39}i \)
3. \((-7i) \cdot (6+5i)= -42 i-35i^2 = \color{red}{35}\color{blue}{-42i}\)
4. \((+4i) \cdot (8-4i)= +32 i-16i^2 = \color{red}{16}\color{blue}{+32i}\)
5. \((7+5i) \cdot (-7-9i)= -49-63i -35 i-45i^2 = -49-63i -35 i+45= \color{red}{-49+45}\color{blue}{-63i -35i}=\color{red}{-4}\color{blue}{-98i}\)
6. \((-6+9i)\cdot (+5i)= -30 i+45i^2 = \color{red}{-45}\color{blue}{-30i}\)
7. \((6+6i) \cdot (2+9i)= 12+54i +12 i+54i^2 = 12+54i +12 i-54= \color{red}{12-54}\color{blue}{+54i +12i}=\color{red}{-42}\color{blue}{+66i}\)
8. \((+5i) \cdot (3+6i)= +15 i+30i^2 = \color{red}{-30}\color{blue}{+15i}\)
9. \((9-7i) \cdot (-2+9i)= -18+81i +14 i-63i^2 = -18+81i +14 i+63= \color{red}{-18+63}\color{blue}{+81i +14i}=\color{red}{45}\color{blue}{+95i}\)
10. \(\frac{-3-7i}{-1+i}= \frac{-3-7i}{-1+i} \cdot \frac{-1-i}{-1-i} = \frac{3+3i +7 i+7i^2 }{(-1)^2-(1i)^2} = \frac{3+3i +7 i-7}{1 + 1} = \frac{-4+10i }{2} = -2- -5i\)
11. \((-2+2i)\cdot (+4i)= -8 i+8i^2 = \color{red}{-8}\color{blue}{-8i}\)
12. \((+5i) \cdot (2+4i)= +10 i+20i^2 = \color{red}{-20}\color{blue}{+10i}\)