Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-10-10i}{10+6i}= \frac{-10-10i}{10+6i} \cdot \frac{10-6i}{10-6i} = \frac{-100+60i -100 i+60i^2 }{(10)^2-(6i)^2} = \frac{-100+60i -100 i-60}{100 + 36} = \frac{-160-40i }{136} = \frac{-20}{17} + \frac{-5}{17}i \)
2. \((3+3i) \cdot (-7-2i)= -21-6i -21 i-6i^2 = -21-6i -21 i+6= \color{red}{-21+6}\color{blue}{-6i -21i}=\color{red}{-15}\color{blue}{-27i}\)
3. \((-9+8i) \cdot (-4-4i)= 36+36i -32 i-32i^2 = 36+36i -32 i+32= \color{red}{36+32}\color{blue}{+36i -32i}=\color{red}{68}\color{blue}{+4i}\)
4. \((+5i) \cdot (7-5i)= +35 i-25i^2 = \color{red}{25}\color{blue}{+35i}\)
5. \((6+8i)\cdot (-4i)= -24 i-32i^2 = \color{red}{32}\color{blue}{-24i}\)
6. \((-2-8i) \cdot (-3+5i)= 6-10i +24 i-40i^2 = 6-10i +24 i+40= \color{red}{6+40}\color{blue}{-10i +24i}=\color{red}{46}\color{blue}{+14i}\)
7. \(\frac{-8-7i}{-1-i}= \frac{-8-7i}{-1-i} \cdot \frac{-1+i}{-1+i} = \frac{8-8i +7 i-7i^2 }{(-1)^2-(-1i)^2} = \frac{8-8i +7 i+7}{1 + 1} = \frac{15-i }{2} = \frac{15}{2} + \frac{-1}{2}i \)
8. \(\frac{7+5i}{6-10i}= \frac{7+5i}{6-10i} \cdot \frac{6+10i}{6+10i} = \frac{42+70i +30 i+50i^2 }{(6)^2-(-10i)^2} = \frac{42+70i +30 i-50}{36 + 100} = \frac{-8+100i }{136} = \frac{-1}{17} - \frac{-25}{34}i \)
9. \(\frac{-2+4i}{5+10i}= \frac{-2+4i}{5+10i} \cdot \frac{5-10i}{5-10i} = \frac{-10+20i +20 i-40i^2 }{(5)^2-(10i)^2} = \frac{-10+20i +20 i+40}{25 + 100} = \frac{30+40i }{125} = \frac{6}{25} - \frac{-8}{25}i \)
10. \((-5-6i) \cdot (-6-5i)= 30+25i +36 i+30i^2 = 30+25i +36 i-30= \color{red}{30-30}\color{blue}{+25i +36i}=\color{blue}{61i}\)
11. \(\frac{6+7i}{-10+9i}= \frac{6+7i}{-10+9i} \cdot \frac{-10-9i}{-10-9i} = \frac{-60-54i -70 i-63i^2 }{(-10)^2-(9i)^2} = \frac{-60-54i -70 i+63}{100 + 81} = \frac{3-124i }{181} = \frac{3}{181} + \frac{-124}{181}i \)
12. \((-4-3i)\cdot (+2i)= -8 i-6i^2 = \color{red}{6}\color{blue}{-8i}\)