Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8i) \cdot (7+10i)= -56 i-80i^2 = \color{red}{80}\color{blue}{-56i}\)
2. \((-3i) \cdot (-6-10i)= +18 i+30i^2 = \color{red}{-30}\color{blue}{+18i}\)
3. \(\frac{3+10i}{-4-8i}= \frac{3+10i}{-4-8i} \cdot \frac{-4+8i}{-4+8i} = \frac{-12+24i -40 i+80i^2 }{(-4)^2-(-8i)^2} = \frac{-12+24i -40 i-80}{16 + 64} = \frac{-92-16i }{80} = \frac{-23}{20} + \frac{-1}{5}i \)
4. \(\frac{10-3i}{-1-2i}= \frac{10-3i}{-1-2i} \cdot \frac{-1+2i}{-1+2i} = \frac{-10+20i +3 i-6i^2 }{(-1)^2-(-2i)^2} = \frac{-10+20i +3 i+6}{1 + 4} = \frac{-4+23i }{5} = \frac{-4}{5} - \frac{-23}{5}i \)
5. \(\frac{-1-10i}{-7-9i}= \frac{-1-10i}{-7-9i} \cdot \frac{-7+9i}{-7+9i} = \frac{7-9i +70 i-90i^2 }{(-7)^2-(-9i)^2} = \frac{7-9i +70 i+90}{49 + 81} = \frac{97+61i }{130} = \frac{97}{130} - \frac{-61}{130}i \)
6. \((-8+8i)\cdot (-5i)= +40 i-40i^2 = \color{red}{40}\color{blue}{+40i}\)
7. \((4+5i) \cdot (4+2i)= 16+8i +20 i+10i^2 = 16+8i +20 i-10= \color{red}{16-10}\color{blue}{+8i +20i}=\color{red}{6}\color{blue}{+28i}\)
8. \((2-9i)\cdot (+8i)= +16 i-72i^2 = \color{red}{72}\color{blue}{+16i}\)
9. \((-5-7i)\cdot (-i)= +5 i+7i^2 = \color{red}{-7}\color{blue}{+5i}\)
10. \(\frac{6-7i}{-10-4i}= \frac{6-7i}{-10-4i} \cdot \frac{-10+4i}{-10+4i} = \frac{-60+24i +70 i-28i^2 }{(-10)^2-(-4i)^2} = \frac{-60+24i +70 i+28}{100 + 16} = \frac{-32+94i }{116} = \frac{-8}{29} - \frac{-47}{58}i \)
11. \(\frac{-9+7i}{-9+6i}= \frac{-9+7i}{-9+6i} \cdot \frac{-9-6i}{-9-6i} = \frac{81+54i -63 i-42i^2 }{(-9)^2-(6i)^2} = \frac{81+54i -63 i+42}{81 + 36} = \frac{123-9i }{117} = \frac{41}{39} + \frac{-1}{13}i \)
12. \((-8i) \cdot (-8-4i)= +64 i+32i^2 = \color{red}{-32}\color{blue}{+64i}\)