Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-2+7i) \cdot (9+10i)= -18-20i +63 i+70i^2 = -18-20i +63 i-70= \color{red}{-18-70}\color{blue}{-20i +63i}=\color{red}{-88}\color{blue}{+43i}\)
2. \((1+3i)\cdot (-i)= -1 i-3i^2 = \color{red}{3}\color{blue}{-i}\)
3. \((5-6i) \cdot (-10-i)= -50-5i +60 i+6i^2 = -50-5i +60 i-6= \color{red}{-50-6}\color{blue}{-5i +60i}=\color{red}{-56}\color{blue}{+55i}\)
4. \((+i) \cdot (5+2i)= +5 i+2i^2 = \color{red}{-2}\color{blue}{+5i}\)
5. \((10+7i) \cdot (-6+4i)= -60+40i -42 i+28i^2 = -60+40i -42 i-28= \color{red}{-60-28}\color{blue}{+40i -42i}=\color{red}{-88}\color{blue}{-2i}\)
6. \(\frac{4+2i}{-3+6i}= \frac{4+2i}{-3+6i} \cdot \frac{-3-6i}{-3-6i} = \frac{-12-24i -6 i-12i^2 }{(-3)^2-(6i)^2} = \frac{-12-24i -6 i+12}{9 + 36} = \frac{0-30i }{45} = 0+ \frac{-2}{3}i \)
7. \((5-5i) \cdot (4+8i)= 20+40i -20 i-40i^2 = 20+40i -20 i+40= \color{red}{20+40}\color{blue}{+40i -20i}=\color{red}{60}\color{blue}{+20i}\)
8. \((7-6i) \cdot (-7-2i)= -49-14i +42 i+12i^2 = -49-14i +42 i-12= \color{red}{-49-12}\color{blue}{-14i +42i}=\color{red}{-61}\color{blue}{+28i}\)
9. \(\frac{-9+7i}{-7+6i}= \frac{-9+7i}{-7+6i} \cdot \frac{-7-6i}{-7-6i} = \frac{63+54i -49 i-42i^2 }{(-7)^2-(6i)^2} = \frac{63+54i -49 i+42}{49 + 36} = \frac{105+5i }{85} = \frac{21}{17} - \frac{-1}{17}i \)
10. \(\frac{2+10i}{-3-7i}= \frac{2+10i}{-3-7i} \cdot \frac{-3+7i}{-3+7i} = \frac{-6+14i -30 i+70i^2 }{(-3)^2-(-7i)^2} = \frac{-6+14i -30 i-70}{9 + 49} = \frac{-76-16i }{58} = \frac{-38}{29} + \frac{-8}{29}i \)
11. \(\frac{-8+4i}{6+9i}= \frac{-8+4i}{6+9i} \cdot \frac{6-9i}{6-9i} = \frac{-48+72i +24 i-36i^2 }{(6)^2-(9i)^2} = \frac{-48+72i +24 i+36}{36 + 81} = \frac{-12+96i }{117} = \frac{-4}{39} - \frac{-32}{39}i \)
12. \((-7-i)\cdot (-2i)= +14 i+2i^2 = \color{red}{-2}\color{blue}{+14i}\)