Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((2-i) \cdot (-6+i)= -12+2i +6 i-i^2 = -12+2i +6 i+= \color{red}{-12+1}\color{blue}{+2i +6i}=\color{red}{-11}\color{blue}{+8i}\)
2. \(\frac{5+3i}{-2-7i}= \frac{5+3i}{-2-7i} \cdot \frac{-2+7i}{-2+7i} = \frac{-10+35i -6 i+21i^2 }{(-2)^2-(-7i)^2} = \frac{-10+35i -6 i-21}{4 + 49} = \frac{-31+29i }{53} = \frac{-31}{53} - \frac{-29}{53}i \)
3. \((-9+5i)\cdot (+10i)= -90 i+50i^2 = \color{red}{-50}\color{blue}{-90i}\)
4. \((-8+9i) \cdot (-7-9i)= 56+72i -63 i-81i^2 = 56+72i -63 i+81= \color{red}{56+81}\color{blue}{+72i -63i}=\color{red}{137}\color{blue}{+9i}\)
5. \((2+2i) \cdot (-2+5i)= -4+10i -4 i+10i^2 = -4+10i -4 i-10= \color{red}{-4-10}\color{blue}{+10i -4i}=\color{red}{-14}\color{blue}{+6i}\)
6. \(\frac{2+6i}{-6-3i}= \frac{2+6i}{-6-3i} \cdot \frac{-6+3i}{-6+3i} = \frac{-12+6i -36 i+18i^2 }{(-6)^2-(-3i)^2} = \frac{-12+6i -36 i-18}{36 + 9} = \frac{-30-30i }{45} = \frac{-2}{3} + \frac{-2}{3}i \)
7. \(\frac{-1+10i}{-8+7i}= \frac{-1+10i}{-8+7i} \cdot \frac{-8-7i}{-8-7i} = \frac{8+7i -80 i-70i^2 }{(-8)^2-(7i)^2} = \frac{8+7i -80 i+70}{64 + 49} = \frac{78-73i }{113} = \frac{78}{113} + \frac{-73}{113}i \)
8. \((5+6i) \cdot (3+5i)= 15+25i +18 i+30i^2 = 15+25i +18 i-30= \color{red}{15-30}\color{blue}{+25i +18i}=\color{red}{-15}\color{blue}{+43i}\)
9. \(\frac{-10+3i}{-5-2i}= \frac{-10+3i}{-5-2i} \cdot \frac{-5+2i}{-5+2i} = \frac{50-20i -15 i+6i^2 }{(-5)^2-(-2i)^2} = \frac{50-20i -15 i-6}{25 + 4} = \frac{44-35i }{29} = \frac{44}{29} + \frac{-35}{29}i \)
10. \((7+5i) \cdot (-9+i)= -63+7i -45 i+5i^2 = -63+7i -45 i-5= \color{red}{-63-5}\color{blue}{+7i -45i}=\color{red}{-68}\color{blue}{-38i}\)
11. \(\frac{-4-3i}{6-10i}= \frac{-4-3i}{6-10i} \cdot \frac{6+10i}{6+10i} = \frac{-24-40i -18 i-30i^2 }{(6)^2-(-10i)^2} = \frac{-24-40i -18 i+30}{36 + 100} = \frac{6-58i }{136} = \frac{3}{68} + \frac{-29}{68}i \)
12. \(\frac{-2-4i}{3-5i}= \frac{-2-4i}{3-5i} \cdot \frac{3+5i}{3+5i} = \frac{-6-10i -12 i-20i^2 }{(3)^2-(-5i)^2} = \frac{-6-10i -12 i+20}{9 + 25} = \frac{14-22i }{34} = \frac{7}{17} + \frac{-11}{17}i \)