Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{7-9i}{-9-7i}= \frac{7-9i}{-9-7i} \cdot \frac{-9+7i}{-9+7i} = \frac{-63+49i +81 i-63i^2 }{(-9)^2-(-7i)^2} = \frac{-63+49i +81 i+63}{81 + 49} = \frac{0+130i }{130} = 0- -1i\)
2. \(\frac{10+5i}{3+6i}= \frac{10+5i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{30-60i +15 i-30i^2 }{(3)^2-(6i)^2} = \frac{30-60i +15 i+30}{9 + 36} = \frac{60-45i }{45} = \frac{4}{3} + 1i\)
3. \(\frac{-7-4i}{-5-5i}= \frac{-7-4i}{-5-5i} \cdot \frac{-5+5i}{-5+5i} = \frac{35-35i +20 i-20i^2 }{(-5)^2-(-5i)^2} = \frac{35-35i +20 i+20}{25 + 25} = \frac{55-15i }{50} = \frac{11}{10} + \frac{-3}{10}i \)
4. \(\frac{-7-2i}{-5+i}= \frac{-7-2i}{-5+i} \cdot \frac{-5-i}{-5-i} = \frac{35+7i +10 i+2i^2 }{(-5)^2-(1i)^2} = \frac{35+7i +10 i-2}{25 + 1} = \frac{33+17i }{26} = \frac{33}{26} - \frac{-17}{26}i \)
5. \((+i) \cdot (-4+10i)= -4 i+10i^2 = \color{red}{-10}\color{blue}{-4i}\)
6. \((-3-10i)\cdot (+10i)= -30 i-100i^2 = \color{red}{100}\color{blue}{-30i}\)
7. \((-3+3i) \cdot (1-3i)= -3+9i +3 i-9i^2 = -3+9i +3 i+9= \color{red}{-3+9}\color{blue}{+9i +3i}=\color{red}{6}\color{blue}{+12i}\)
8. \((-4i) \cdot (-5-10i)= +20 i+40i^2 = \color{red}{-40}\color{blue}{+20i}\)
9. \(\frac{-6+8i}{-6-2i}= \frac{-6+8i}{-6-2i} \cdot \frac{-6+2i}{-6+2i} = \frac{36-12i -48 i+16i^2 }{(-6)^2-(-2i)^2} = \frac{36-12i -48 i-16}{36 + 4} = \frac{20-60i }{40} = \frac{1}{2} + \frac{-3}{2}i \)
10. \((+4i) \cdot (-4-8i)= -16 i-32i^2 = \color{red}{32}\color{blue}{-16i}\)
11. \((1+10i) \cdot (-7-4i)= -7-4i -70 i-40i^2 = -7-4i -70 i+40= \color{red}{-7+40}\color{blue}{-4i -70i}=\color{red}{33}\color{blue}{-74i}\)
12. \((7-4i) \cdot (3-i)= 21-7i -12 i+4i^2 = 21-7i -12 i-4= \color{red}{21-4}\color{blue}{-7i -12i}=\color{red}{17}\color{blue}{-19i}\)