Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-4+3i) \cdot (-3-i)= 12+4i -9 i-3i^2 = 12+4i -9 i+3= \color{red}{12+3}\color{blue}{+4i -9i}=\color{red}{15}\color{blue}{-5i}\)
2. \((+4i) \cdot (1-4i)= +4 i-16i^2 = \color{red}{16}\color{blue}{+4i}\)
3. \((5+8i)\cdot (-6i)= -30 i-48i^2 = \color{red}{48}\color{blue}{-30i}\)
4. \(\frac{7-4i}{-7+7i}= \frac{7-4i}{-7+7i} \cdot \frac{-7-7i}{-7-7i} = \frac{-49-49i +28 i+28i^2 }{(-7)^2-(7i)^2} = \frac{-49-49i +28 i-28}{49 + 49} = \frac{-77-21i }{98} = \frac{-11}{14} + \frac{-3}{14}i \)
5. \((-10-i) \cdot (10+5i)= -100-50i -10 i-5i^2 = -100-50i -10 i+5= \color{red}{-100+5}\color{blue}{-50i -10i}=\color{red}{-95}\color{blue}{-60i}\)
6. \((9+5i) \cdot (-7-4i)= -63-36i -35 i-20i^2 = -63-36i -35 i+20= \color{red}{-63+20}\color{blue}{-36i -35i}=\color{red}{-43}\color{blue}{-71i}\)
7. \((+i) \cdot (2-3i)= +2 i-3i^2 = \color{red}{3}\color{blue}{+2i}\)
8. \((-8i) \cdot (1+2i)= -8 i-16i^2 = \color{red}{16}\color{blue}{-8i}\)
9. \((-2+6i) \cdot (-5+4i)= 10-8i -30 i+24i^2 = 10-8i -30 i-24= \color{red}{10-24}\color{blue}{-8i -30i}=\color{red}{-14}\color{blue}{-38i}\)
10. \((-9+3i)\cdot (+9i)= -81 i+27i^2 = \color{red}{-27}\color{blue}{-81i}\)
11. \((2-10i) \cdot (-3-2i)= -6-4i +30 i+20i^2 = -6-4i +30 i-20= \color{red}{-6-20}\color{blue}{-4i +30i}=\color{red}{-26}\color{blue}{+26i}\)
12. \((9+6i) \cdot (4-7i)= 36-63i +24 i-42i^2 = 36-63i +24 i+42= \color{red}{36+42}\color{blue}{-63i +24i}=\color{red}{78}\color{blue}{-39i}\)