Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-2+6i) \cdot (7-8i)= -14+16i +42 i-48i^2 = -14+16i +42 i+48= \color{red}{-14+48}\color{blue}{+16i +42i}=\color{red}{34}\color{blue}{+58i}\)
2. \((8+5i)\cdot (+8i)= +64 i+40i^2 = \color{red}{-40}\color{blue}{+64i}\)
3. \((-7+6i) \cdot (3+8i)= -21-56i +18 i+48i^2 = -21-56i +18 i-48= \color{red}{-21-48}\color{blue}{-56i +18i}=\color{red}{-69}\color{blue}{-38i}\)
4. \((-6-2i) \cdot (-8-8i)= 48+48i +16 i+16i^2 = 48+48i +16 i-16= \color{red}{48-16}\color{blue}{+48i +16i}=\color{red}{32}\color{blue}{+64i}\)
5. \((-2+i) \cdot (8+5i)= -16-10i +8 i+5i^2 = -16-10i +8 i-5= \color{red}{-16-5}\color{blue}{-10i +8i}=\color{red}{-21}\color{blue}{-2i}\)
6. \(\frac{2+7i}{-5+10i}= \frac{2+7i}{-5+10i} \cdot \frac{-5-10i}{-5-10i} = \frac{-10-20i -35 i-70i^2 }{(-5)^2-(10i)^2} = \frac{-10-20i -35 i+70}{25 + 100} = \frac{60-55i }{125} = \frac{12}{25} + \frac{-11}{25}i \)
7. \((1+4i)\cdot (+i)= +1 i+4i^2 = \color{red}{-4}\color{blue}{+i}\)
8. \((+4i) \cdot (7+3i)= +28 i+12i^2 = \color{red}{-12}\color{blue}{+28i}\)
9. \((6-6i)\cdot (+9i)= +54 i-54i^2 = \color{red}{54}\color{blue}{+54i}\)
10. \(\frac{10+2i}{-10-2i}= \frac{10+2i}{-10-2i} \cdot \frac{-10+2i}{-10+2i} = \frac{-100+20i -20 i+4i^2 }{(-10)^2-(-2i)^2} = \frac{-100+20i -20 i-4}{100 + 4} = \frac{-104+0i }{104} = -1+ 0i\)
11. \((-4+7i) \cdot (-10-6i)= 40+24i -70 i-42i^2 = 40+24i -70 i+42= \color{red}{40+42}\color{blue}{+24i -70i}=\color{red}{82}\color{blue}{-46i}\)
12. \(\frac{10-3i}{-9-10i}= \frac{10-3i}{-9-10i} \cdot \frac{-9+10i}{-9+10i} = \frac{-90+100i +27 i-30i^2 }{(-9)^2-(-10i)^2} = \frac{-90+100i +27 i+30}{81 + 100} = \frac{-60+127i }{181} = \frac{-60}{181} - \frac{-127}{181}i \)