Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9-7i) \cdot (5-5i)= -45+45i -35 i+35i^2 = -45+45i -35 i-35= \color{red}{-45-35}\color{blue}{+45i -35i}=\color{red}{-80}\color{blue}{+10i}\)
2. \((-7-i)\cdot (+3i)= -21 i-3i^2 = \color{red}{3}\color{blue}{-21i}\)
3. \((+i) \cdot (-8+4i)= -8 i+4i^2 = \color{red}{-4}\color{blue}{-8i}\)
4. \(\frac{8+10i}{9+10i}= \frac{8+10i}{9+10i} \cdot \frac{9-10i}{9-10i} = \frac{72-80i +90 i-100i^2 }{(9)^2-(10i)^2} = \frac{72-80i +90 i+100}{81 + 100} = \frac{172+10i }{181} = \frac{172}{181} - \frac{-10}{181}i \)
5. \((-1-9i) \cdot (7-5i)= -7+5i -63 i+45i^2 = -7+5i -63 i-45= \color{red}{-7-45}\color{blue}{+5i -63i}=\color{red}{-52}\color{blue}{-58i}\)
6. \((+8i) \cdot (-3+10i)= -24 i+80i^2 = \color{red}{-80}\color{blue}{-24i}\)
7. \((+8i) \cdot (-6-7i)= -48 i-56i^2 = \color{red}{56}\color{blue}{-48i}\)
8. \((-7-2i) \cdot (-3-i)= 21+7i +6 i+2i^2 = 21+7i +6 i-2= \color{red}{21-2}\color{blue}{+7i +6i}=\color{red}{19}\color{blue}{+13i}\)
9. \((-6-i) \cdot (-6+3i)= 36-18i +6 i-3i^2 = 36-18i +6 i+3= \color{red}{36+3}\color{blue}{-18i +6i}=\color{red}{39}\color{blue}{-12i}\)
10. \((6-5i) \cdot (-2-6i)= -12-36i +10 i+30i^2 = -12-36i +10 i-30= \color{red}{-12-30}\color{blue}{-36i +10i}=\color{red}{-42}\color{blue}{-26i}\)
11. \(\frac{10+3i}{-5+4i}= \frac{10+3i}{-5+4i} \cdot \frac{-5-4i}{-5-4i} = \frac{-50-40i -15 i-12i^2 }{(-5)^2-(4i)^2} = \frac{-50-40i -15 i+12}{25 + 16} = \frac{-38-55i }{41} = \frac{-38}{41} + \frac{-55}{41}i \)
12. \((10+5i)\cdot (+9i)= +90 i+45i^2 = \color{red}{-45}\color{blue}{+90i}\)