Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7+4i) \cdot (-7+2i)= 49-14i -28 i+8i^2 = 49-14i -28 i-8= \color{red}{49-8}\color{blue}{-14i -28i}=\color{red}{41}\color{blue}{-42i}\)
2. \(\frac{5+6i}{-6+4i}= \frac{5+6i}{-6+4i} \cdot \frac{-6-4i}{-6-4i} = \frac{-30-20i -36 i-24i^2 }{(-6)^2-(4i)^2} = \frac{-30-20i -36 i+24}{36 + 16} = \frac{-6-56i }{52} = \frac{-3}{26} + \frac{-14}{13}i \)
3. \((8+3i)\cdot (+6i)= +48 i+18i^2 = \color{red}{-18}\color{blue}{+48i}\)
4. \((6+5i) \cdot (1-10i)= 6-60i +5 i-50i^2 = 6-60i +5 i+50= \color{red}{6+50}\color{blue}{-60i +5i}=\color{red}{56}\color{blue}{-55i}\)
5. \((9-8i)\cdot (-7i)= -63 i+56i^2 = \color{red}{-56}\color{blue}{-63i}\)
6. \((+8i) \cdot (3-9i)= +24 i-72i^2 = \color{red}{72}\color{blue}{+24i}\)
7. \(\frac{5-6i}{9+10i}= \frac{5-6i}{9+10i} \cdot \frac{9-10i}{9-10i} = \frac{45-50i -54 i+60i^2 }{(9)^2-(10i)^2} = \frac{45-50i -54 i-60}{81 + 100} = \frac{-15-104i }{181} = \frac{-15}{181} + \frac{-104}{181}i \)
8. \((-2-i)\cdot (-2i)= +4 i+2i^2 = \color{red}{-2}\color{blue}{+4i}\)
9. \((-3-6i) \cdot (9-3i)= -27+9i -54 i+18i^2 = -27+9i -54 i-18= \color{red}{-27-18}\color{blue}{+9i -54i}=\color{red}{-45}\color{blue}{-45i}\)
10. \((-2i) \cdot (-4+10i)= +8 i-20i^2 = \color{red}{20}\color{blue}{+8i}\)
11. \(\frac{-1+3i}{-2+5i}= \frac{-1+3i}{-2+5i} \cdot \frac{-2-5i}{-2-5i} = \frac{2+5i -6 i-15i^2 }{(-2)^2-(5i)^2} = \frac{2+5i -6 i+15}{4 + 25} = \frac{17-i }{29} = \frac{17}{29} + \frac{-1}{29}i \)
12. \(\frac{2-10i}{6+2i}= \frac{2-10i}{6+2i} \cdot \frac{6-2i}{6-2i} = \frac{12-4i -60 i+20i^2 }{(6)^2-(2i)^2} = \frac{12-4i -60 i-20}{36 + 4} = \frac{-8-64i }{40} = \frac{-1}{5} + \frac{-8}{5}i \)