Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{1-8i}{2-7i}= \frac{1-8i}{2-7i} \cdot \frac{2+7i}{2+7i} = \frac{2+7i -16 i-56i^2 }{(2)^2-(-7i)^2} = \frac{2+7i -16 i+56}{4 + 49} = \frac{58-9i }{53} = \frac{58}{53} + \frac{-9}{53}i \)
2. \((9-4i)\cdot (-3i)= -27 i+12i^2 = \color{red}{-12}\color{blue}{-27i}\)
3. \((-4-10i) \cdot (5-2i)= -20+8i -50 i+20i^2 = -20+8i -50 i-20= \color{red}{-20-20}\color{blue}{+8i -50i}=\color{red}{-40}\color{blue}{-42i}\)
4. \((-3-10i) \cdot (4-2i)= -12+6i -40 i+20i^2 = -12+6i -40 i-20= \color{red}{-12-20}\color{blue}{+6i -40i}=\color{red}{-32}\color{blue}{-34i}\)
5. \((1-4i) \cdot (10+4i)= 10+4i -40 i-16i^2 = 10+4i -40 i+16= \color{red}{10+16}\color{blue}{+4i -40i}=\color{red}{26}\color{blue}{-36i}\)
6. \((-5i) \cdot (-1-4i)= +5 i+20i^2 = \color{red}{-20}\color{blue}{+5i}\)
7. \((+3i) \cdot (-6+9i)= -18 i+27i^2 = \color{red}{-27}\color{blue}{-18i}\)
8. \(\frac{-5-4i}{-8+7i}= \frac{-5-4i}{-8+7i} \cdot \frac{-8-7i}{-8-7i} = \frac{40+35i +32 i+28i^2 }{(-8)^2-(7i)^2} = \frac{40+35i +32 i-28}{64 + 49} = \frac{12+67i }{113} = \frac{12}{113} - \frac{-67}{113}i \)
9. \((+7i) \cdot (10+6i)= +70 i+42i^2 = \color{red}{-42}\color{blue}{+70i}\)
10. \(\frac{-2-5i}{-8+i}= \frac{-2-5i}{-8+i} \cdot \frac{-8-i}{-8-i} = \frac{16+2i +40 i+5i^2 }{(-8)^2-(1i)^2} = \frac{16+2i +40 i-5}{64 + 1} = \frac{11+42i }{65} = \frac{11}{65} - \frac{-42}{65}i \)
11. \((10-6i) \cdot (5-3i)= 50-30i -30 i+18i^2 = 50-30i -30 i-18= \color{red}{50-18}\color{blue}{-30i -30i}=\color{red}{32}\color{blue}{-60i}\)
12. \((5+2i) \cdot (-5+10i)= -25+50i -10 i+20i^2 = -25+50i -10 i-20= \color{red}{-25-20}\color{blue}{+50i -10i}=\color{red}{-45}\color{blue}{+40i}\)