Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+9i) \cdot (4-6i)= +36 i-54i^2 = \color{red}{54}\color{blue}{+36i}\)
2. \(\frac{4-6i}{7+3i}= \frac{4-6i}{7+3i} \cdot \frac{7-3i}{7-3i} = \frac{28-12i -42 i+18i^2 }{(7)^2-(3i)^2} = \frac{28-12i -42 i-18}{49 + 9} = \frac{10-54i }{58} = \frac{5}{29} + \frac{-27}{29}i \)
3. \((-7i) \cdot (-5+7i)= +35 i-49i^2 = \color{red}{49}\color{blue}{+35i}\)
4. \((2-8i) \cdot (-5+9i)= -10+18i +40 i-72i^2 = -10+18i +40 i+72= \color{red}{-10+72}\color{blue}{+18i +40i}=\color{red}{62}\color{blue}{+58i}\)
5. \((6+8i)\cdot (+8i)= +48 i+64i^2 = \color{red}{-64}\color{blue}{+48i}\)
6. \((2-4i) \cdot (-10-8i)= -20-16i +40 i+32i^2 = -20-16i +40 i-32= \color{red}{-20-32}\color{blue}{-16i +40i}=\color{red}{-52}\color{blue}{+24i}\)
7. \(\frac{1+6i}{10+10i}= \frac{1+6i}{10+10i} \cdot \frac{10-10i}{10-10i} = \frac{10-10i +60 i-60i^2 }{(10)^2-(10i)^2} = \frac{10-10i +60 i+60}{100 + 100} = \frac{70+50i }{200} = \frac{7}{20} - \frac{-1}{4}i \)
8. \((3-6i)\cdot (-3i)= -9 i+18i^2 = \color{red}{-18}\color{blue}{-9i}\)
9. \((-6-5i) \cdot (-4+7i)= 24-42i +20 i-35i^2 = 24-42i +20 i+35= \color{red}{24+35}\color{blue}{-42i +20i}=\color{red}{59}\color{blue}{-22i}\)
10. \(\frac{-5+7i}{1+3i}= \frac{-5+7i}{1+3i} \cdot \frac{1-3i}{1-3i} = \frac{-5+15i +7 i-21i^2 }{(1)^2-(3i)^2} = \frac{-5+15i +7 i+21}{1 + 9} = \frac{16+22i }{10} = \frac{8}{5} - \frac{-11}{5}i \)
11. \((+7i) \cdot (-1+5i)= -7 i+35i^2 = \color{red}{-35}\color{blue}{-7i}\)
12. \(\frac{-6+5i}{-3-5i}= \frac{-6+5i}{-3-5i} \cdot \frac{-3+5i}{-3+5i} = \frac{18-30i -15 i+25i^2 }{(-3)^2-(-5i)^2} = \frac{18-30i -15 i-25}{9 + 25} = \frac{-7-45i }{34} = \frac{-7}{34} + \frac{-45}{34}i \)