Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7-9i) \cdot (-8-3i)= 56+21i +72 i+27i^2 = 56+21i +72 i-27= \color{red}{56-27}\color{blue}{+21i +72i}=\color{red}{29}\color{blue}{+93i}\)
2. \((+9i) \cdot (-5+9i)= -45 i+81i^2 = \color{red}{-81}\color{blue}{-45i}\)
3. \(\frac{-2+7i}{8+i}= \frac{-2+7i}{8+i} \cdot \frac{8-i}{8-i} = \frac{-16+2i +56 i-7i^2 }{(8)^2-(1i)^2} = \frac{-16+2i +56 i+7}{64 + 1} = \frac{-9+58i }{65} = \frac{-9}{65} - \frac{-58}{65}i \)
4. \(\frac{2-2i}{2+6i}= \frac{2-2i}{2+6i} \cdot \frac{2-6i}{2-6i} = \frac{4-12i -4 i+12i^2 }{(2)^2-(6i)^2} = \frac{4-12i -4 i-12}{4 + 36} = \frac{-8-16i }{40} = \frac{-1}{5} + \frac{-2}{5}i \)
5. \(\frac{-3-7i}{4-8i}= \frac{-3-7i}{4-8i} \cdot \frac{4+8i}{4+8i} = \frac{-12-24i -28 i-56i^2 }{(4)^2-(-8i)^2} = \frac{-12-24i -28 i+56}{16 + 64} = \frac{44-52i }{80} = \frac{11}{20} + \frac{-13}{20}i \)
6. \((3+8i) \cdot (6-i)= 18-3i +48 i-8i^2 = 18-3i +48 i+8= \color{red}{18+8}\color{blue}{-3i +48i}=\color{red}{26}\color{blue}{+45i}\)
7. \((-9+7i) \cdot (7-i)= -63+9i +49 i-7i^2 = -63+9i +49 i+7= \color{red}{-63+7}\color{blue}{+9i +49i}=\color{red}{-56}\color{blue}{+58i}\)
8. \(\frac{-6-10i}{-1+i}= \frac{-6-10i}{-1+i} \cdot \frac{-1-i}{-1-i} = \frac{6+6i +10 i+10i^2 }{(-1)^2-(1i)^2} = \frac{6+6i +10 i-10}{1 + 1} = \frac{-4+16i }{2} = -2- -8i\)
9. \((-8-7i)\cdot (-4i)= +32 i+28i^2 = \color{red}{-28}\color{blue}{+32i}\)
10. \((2+4i) \cdot (8+3i)= 16+6i +32 i+12i^2 = 16+6i +32 i-12= \color{red}{16-12}\color{blue}{+6i +32i}=\color{red}{4}\color{blue}{+38i}\)
11. \(\frac{-5+4i}{9-10i}= \frac{-5+4i}{9-10i} \cdot \frac{9+10i}{9+10i} = \frac{-45-50i +36 i+40i^2 }{(9)^2-(-10i)^2} = \frac{-45-50i +36 i-40}{81 + 100} = \frac{-85-14i }{181} = \frac{-85}{181} + \frac{-14}{181}i \)
12. \(\frac{6+3i}{-8+6i}= \frac{6+3i}{-8+6i} \cdot \frac{-8-6i}{-8-6i} = \frac{-48-36i -24 i-18i^2 }{(-8)^2-(6i)^2} = \frac{-48-36i -24 i+18}{64 + 36} = \frac{-30-60i }{100} = \frac{-3}{10} + \frac{-3}{5}i \)