Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-10+9i}{-7-10i}= \frac{-10+9i}{-7-10i} \cdot \frac{-7+10i}{-7+10i} = \frac{70-100i -63 i+90i^2 }{(-7)^2-(-10i)^2} = \frac{70-100i -63 i-90}{49 + 100} = \frac{-20-163i }{149} = \frac{-20}{149} + \frac{-163}{149}i \)
2. \(\frac{-2+2i}{-6-i}= \frac{-2+2i}{-6-i} \cdot \frac{-6+i}{-6+i} = \frac{12-2i -12 i+2i^2 }{(-6)^2-(-1i)^2} = \frac{12-2i -12 i-2}{36 + 1} = \frac{10-14i }{37} = \frac{10}{37} + \frac{-14}{37}i \)
3. \(\frac{-9-3i}{-2+7i}= \frac{-9-3i}{-2+7i} \cdot \frac{-2-7i}{-2-7i} = \frac{18+63i +6 i+21i^2 }{(-2)^2-(7i)^2} = \frac{18+63i +6 i-21}{4 + 49} = \frac{-3+69i }{53} = \frac{-3}{53} - \frac{-69}{53}i \)
4. \((+8i) \cdot (4-4i)= +32 i-32i^2 = \color{red}{32}\color{blue}{+32i}\)
5. \((-9i) \cdot (-9+6i)= +81 i-54i^2 = \color{red}{54}\color{blue}{+81i}\)
6. \((+2i) \cdot (-4-10i)= -8 i-20i^2 = \color{red}{20}\color{blue}{-8i}\)
7. \(\frac{-3+3i}{8+8i}= \frac{-3+3i}{8+8i} \cdot \frac{8-8i}{8-8i} = \frac{-24+24i +24 i-24i^2 }{(8)^2-(8i)^2} = \frac{-24+24i +24 i+24}{64 + 64} = \frac{0+48i }{128} = 0- \frac{-3}{8}i \)
8. \((-1+8i) \cdot (-5-9i)= 5+9i -40 i-72i^2 = 5+9i -40 i+72= \color{red}{5+72}\color{blue}{+9i -40i}=\color{red}{77}\color{blue}{-31i}\)
9. \((6-9i) \cdot (-4+10i)= -24+60i +36 i-90i^2 = -24+60i +36 i+90= \color{red}{-24+90}\color{blue}{+60i +36i}=\color{red}{66}\color{blue}{+96i}\)
10. \((-4-10i) \cdot (-3+9i)= 12-36i +30 i-90i^2 = 12-36i +30 i+90= \color{red}{12+90}\color{blue}{-36i +30i}=\color{red}{102}\color{blue}{-6i}\)
11. \(\frac{3-i}{8-10i}= \frac{3-i}{8-10i} \cdot \frac{8+10i}{8+10i} = \frac{24+30i -8 i-10i^2 }{(8)^2-(-10i)^2} = \frac{24+30i -8 i+10}{64 + 100} = \frac{34+22i }{164} = \frac{17}{82} - \frac{-11}{82}i \)
12. \((-9-5i) \cdot (-8+10i)= 72-90i +40 i-50i^2 = 72-90i +40 i+50= \color{red}{72+50}\color{blue}{-90i +40i}=\color{red}{122}\color{blue}{-50i}\)