Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1+7i) \cdot (-2+10i)= 2-10i -14 i+70i^2 = 2-10i -14 i-70= \color{red}{2-70}\color{blue}{-10i -14i}=\color{red}{-68}\color{blue}{-24i}\)
2. \((+4i) \cdot (-4-10i)= -16 i-40i^2 = \color{red}{40}\color{blue}{-16i}\)
3. \((3+5i) \cdot (-6+8i)= -18+24i -30 i+40i^2 = -18+24i -30 i-40= \color{red}{-18-40}\color{blue}{+24i -30i}=\color{red}{-58}\color{blue}{-6i}\)
4. \((3+5i) \cdot (6+4i)= 18+12i +30 i+20i^2 = 18+12i +30 i-20= \color{red}{18-20}\color{blue}{+12i +30i}=\color{red}{-2}\color{blue}{+42i}\)
5. \((-10+10i)\cdot (-9i)= +90 i-90i^2 = \color{red}{90}\color{blue}{+90i}\)
6. \((7+5i) \cdot (-8+8i)= -56+56i -40 i+40i^2 = -56+56i -40 i-40= \color{red}{-56-40}\color{blue}{+56i -40i}=\color{red}{-96}\color{blue}{+16i}\)
7. \(\frac{-4+6i}{3+4i}= \frac{-4+6i}{3+4i} \cdot \frac{3-4i}{3-4i} = \frac{-12+16i +18 i-24i^2 }{(3)^2-(4i)^2} = \frac{-12+16i +18 i+24}{9 + 16} = \frac{12+34i }{25} = \frac{12}{25} - \frac{-34}{25}i \)
8. \((8+5i) \cdot (2+i)= 16+8i +10 i+5i^2 = 16+8i +10 i-5= \color{red}{16-5}\color{blue}{+8i +10i}=\color{red}{11}\color{blue}{+18i}\)
9. \(\frac{2-10i}{3-3i}= \frac{2-10i}{3-3i} \cdot \frac{3+3i}{3+3i} = \frac{6+6i -30 i-30i^2 }{(3)^2-(-3i)^2} = \frac{6+6i -30 i+30}{9 + 9} = \frac{36-24i }{18} = 2+ \frac{-4}{3}i \)
10. \(\frac{10-7i}{-7-9i}= \frac{10-7i}{-7-9i} \cdot \frac{-7+9i}{-7+9i} = \frac{-70+90i +49 i-63i^2 }{(-7)^2-(-9i)^2} = \frac{-70+90i +49 i+63}{49 + 81} = \frac{-7+139i }{130} = \frac{-7}{130} - \frac{-139}{130}i \)
11. \(\frac{-5-5i}{8-4i}= \frac{-5-5i}{8-4i} \cdot \frac{8+4i}{8+4i} = \frac{-40-20i -40 i-20i^2 }{(8)^2-(-4i)^2} = \frac{-40-20i -40 i+20}{64 + 16} = \frac{-20-60i }{80} = \frac{-1}{4} + \frac{-3}{4}i \)
12. \((-10i) \cdot (-1-10i)= +10 i+100i^2 = \color{red}{-100}\color{blue}{+10i}\)