Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{8+7i}{4-6i}= \frac{8+7i}{4-6i} \cdot \frac{4+6i}{4+6i} = \frac{32+48i +28 i+42i^2 }{(4)^2-(-6i)^2} = \frac{32+48i +28 i-42}{16 + 36} = \frac{-10+76i }{52} = \frac{-5}{26} - \frac{-19}{13}i \)
2. \((-7-3i) \cdot (6-6i)= -42+42i -18 i+18i^2 = -42+42i -18 i-18= \color{red}{-42-18}\color{blue}{+42i -18i}=\color{red}{-60}\color{blue}{+24i}\)
3. \(\frac{6+3i}{-10-7i}= \frac{6+3i}{-10-7i} \cdot \frac{-10+7i}{-10+7i} = \frac{-60+42i -30 i+21i^2 }{(-10)^2-(-7i)^2} = \frac{-60+42i -30 i-21}{100 + 49} = \frac{-81+12i }{149} = \frac{-81}{149} - \frac{-12}{149}i \)
4. \((+5i) \cdot (10+8i)= +50 i+40i^2 = \color{red}{-40}\color{blue}{+50i}\)
5. \((5-4i) \cdot (-8-4i)= -40-20i +32 i+16i^2 = -40-20i +32 i-16= \color{red}{-40-16}\color{blue}{-20i +32i}=\color{red}{-56}\color{blue}{+12i}\)
6. \((+2i) \cdot (3-8i)= +6 i-16i^2 = \color{red}{16}\color{blue}{+6i}\)
7. \((-7i) \cdot (-9-7i)= +63 i+49i^2 = \color{red}{-49}\color{blue}{+63i}\)
8. \((-8-5i) \cdot (-8+10i)= 64-80i +40 i-50i^2 = 64-80i +40 i+50= \color{red}{64+50}\color{blue}{-80i +40i}=\color{red}{114}\color{blue}{-40i}\)
9. \((3-8i) \cdot (-9+10i)= -27+30i +72 i-80i^2 = -27+30i +72 i+80= \color{red}{-27+80}\color{blue}{+30i +72i}=\color{red}{53}\color{blue}{+102i}\)
10. \((9+6i) \cdot (1+8i)= 9+72i +6 i+48i^2 = 9+72i +6 i-48= \color{red}{9-48}\color{blue}{+72i +6i}=\color{red}{-39}\color{blue}{+78i}\)
11. \((3+5i) \cdot (8+2i)= 24+6i +40 i+10i^2 = 24+6i +40 i-10= \color{red}{24-10}\color{blue}{+6i +40i}=\color{red}{14}\color{blue}{+46i}\)
12. \((7+9i) \cdot (-4-9i)= -28-63i -36 i-81i^2 = -28-63i -36 i+81= \color{red}{-28+81}\color{blue}{-63i -36i}=\color{red}{53}\color{blue}{-99i}\)