Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9+3i) \cdot (10-9i)= -90+81i +30 i-27i^2 = -90+81i +30 i+27= \color{red}{-90+27}\color{blue}{+81i +30i}=\color{red}{-63}\color{blue}{+111i}\)
2. \(\frac{7-7i}{4+10i}= \frac{7-7i}{4+10i} \cdot \frac{4-10i}{4-10i} = \frac{28-70i -28 i+70i^2 }{(4)^2-(10i)^2} = \frac{28-70i -28 i-70}{16 + 100} = \frac{-42-98i }{116} = \frac{-21}{58} + \frac{-49}{58}i \)
3. \((7+i) \cdot (8-2i)= 56-14i +8 i-2i^2 = 56-14i +8 i+2= \color{red}{56+2}\color{blue}{-14i +8i}=\color{red}{58}\color{blue}{-6i}\)
4. \((-2-2i) \cdot (-9+i)= 18-2i +18 i-2i^2 = 18-2i +18 i+2= \color{red}{18+2}\color{blue}{-2i +18i}=\color{red}{20}\color{blue}{+16i}\)
5. \((9+6i) \cdot (4+10i)= 36+90i +24 i+60i^2 = 36+90i +24 i-60= \color{red}{36-60}\color{blue}{+90i +24i}=\color{red}{-24}\color{blue}{+114i}\)
6. \((-9-9i)\cdot (-10i)= +90 i+90i^2 = \color{red}{-90}\color{blue}{+90i}\)
7. \(\frac{3-3i}{3+i}= \frac{3-3i}{3+i} \cdot \frac{3-i}{3-i} = \frac{9-3i -9 i+3i^2 }{(3)^2-(1i)^2} = \frac{9-3i -9 i-3}{9 + 1} = \frac{6-12i }{10} = \frac{3}{5} + \frac{-6}{5}i \)
8. \(\frac{-2+4i}{-1+2i}= \frac{-2+4i}{-1+2i} \cdot \frac{-1-2i}{-1-2i} = \frac{2+4i -4 i-8i^2 }{(-1)^2-(2i)^2} = \frac{2+4i -4 i+8}{1 + 4} = \frac{10+0i }{5} = 2+ 0i\)
9. \((2+i) \cdot (2+8i)= 4+16i +2 i+8i^2 = 4+16i +2 i-8= \color{red}{4-8}\color{blue}{+16i +2i}=\color{red}{-4}\color{blue}{+18i}\)
10. \(\frac{4-10i}{-3-i}= \frac{4-10i}{-3-i} \cdot \frac{-3+i}{-3+i} = \frac{-12+4i +30 i-10i^2 }{(-3)^2-(-1i)^2} = \frac{-12+4i +30 i+10}{9 + 1} = \frac{-2+34i }{10} = \frac{-1}{5} - \frac{-17}{5}i \)
11. \((+10i) \cdot (3-8i)= +30 i-80i^2 = \color{red}{80}\color{blue}{+30i}\)
12. \(\frac{-7+4i}{-3+6i}= \frac{-7+4i}{-3+6i} \cdot \frac{-3-6i}{-3-6i} = \frac{21+42i -12 i-24i^2 }{(-3)^2-(6i)^2} = \frac{21+42i -12 i+24}{9 + 36} = \frac{45+30i }{45} = 1- \frac{-2}{3}i \)