Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{7+7i}{-3-6i}= \frac{7+7i}{-3-6i} \cdot \frac{-3+6i}{-3+6i} = \frac{-21+42i -21 i+42i^2 }{(-3)^2-(-6i)^2} = \frac{-21+42i -21 i-42}{9 + 36} = \frac{-63+21i }{45} = \frac{-7}{5} - \frac{-7}{15}i \)
2. \(\frac{-2-3i}{-2-2i}= \frac{-2-3i}{-2-2i} \cdot \frac{-2+2i}{-2+2i} = \frac{4-4i +6 i-6i^2 }{(-2)^2-(-2i)^2} = \frac{4-4i +6 i+6}{4 + 4} = \frac{10+2i }{8} = \frac{5}{4} - \frac{-1}{4}i \)
3. \((6+8i)\cdot (-10i)= -60 i-80i^2 = \color{red}{80}\color{blue}{-60i}\)
4. \((-7+i) \cdot (4-6i)= -28+42i +4 i-6i^2 = -28+42i +4 i+6= \color{red}{-28+6}\color{blue}{+42i +4i}=\color{red}{-22}\color{blue}{+46i}\)
5. \(\frac{8+2i}{3+i}= \frac{8+2i}{3+i} \cdot \frac{3-i}{3-i} = \frac{24-8i +6 i-2i^2 }{(3)^2-(1i)^2} = \frac{24-8i +6 i+2}{9 + 1} = \frac{26-2i }{10} = \frac{13}{5} + \frac{-1}{5}i \)
6. \(\frac{2-4i}{4-7i}= \frac{2-4i}{4-7i} \cdot \frac{4+7i}{4+7i} = \frac{8+14i -16 i-28i^2 }{(4)^2-(-7i)^2} = \frac{8+14i -16 i+28}{16 + 49} = \frac{36-2i }{65} = \frac{36}{65} + \frac{-2}{65}i \)
7. \(\frac{3+4i}{-10+10i}= \frac{3+4i}{-10+10i} \cdot \frac{-10-10i}{-10-10i} = \frac{-30-30i -40 i-40i^2 }{(-10)^2-(10i)^2} = \frac{-30-30i -40 i+40}{100 + 100} = \frac{10-70i }{200} = \frac{1}{20} + \frac{-7}{20}i \)
8. \((-8+5i) \cdot (3-8i)= -24+64i +15 i-40i^2 = -24+64i +15 i+40= \color{red}{-24+40}\color{blue}{+64i +15i}=\color{red}{16}\color{blue}{+79i}\)
9. \((5+10i)\cdot (-3i)= -15 i-30i^2 = \color{red}{30}\color{blue}{-15i}\)
10. \((-7+i) \cdot (5-6i)= -35+42i +5 i-6i^2 = -35+42i +5 i+6= \color{red}{-35+6}\color{blue}{+42i +5i}=\color{red}{-29}\color{blue}{+47i}\)
11. \((8+i) \cdot (-4+5i)= -32+40i -4 i+5i^2 = -32+40i -4 i-5= \color{red}{-32-5}\color{blue}{+40i -4i}=\color{red}{-37}\color{blue}{+36i}\)
12. \((8+10i) \cdot (-8-8i)= -64-64i -80 i-80i^2 = -64-64i -80 i+80= \color{red}{-64+80}\color{blue}{-64i -80i}=\color{red}{16}\color{blue}{-144i}\)