Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+7i) \cdot (3-3i)= +21 i-21i^2 = \color{red}{21}\color{blue}{+21i}\)
2. \((-3+4i) \cdot (-1-10i)= 3+30i -4 i-40i^2 = 3+30i -4 i+40= \color{red}{3+40}\color{blue}{+30i -4i}=\color{red}{43}\color{blue}{+26i}\)
3. \((-6+3i) \cdot (-4+9i)= 24-54i -12 i+27i^2 = 24-54i -12 i-27= \color{red}{24-27}\color{blue}{-54i -12i}=\color{red}{-3}\color{blue}{-66i}\)
4. \(\frac{-10-7i}{-8-10i}= \frac{-10-7i}{-8-10i} \cdot \frac{-8+10i}{-8+10i} = \frac{80-100i +56 i-70i^2 }{(-8)^2-(-10i)^2} = \frac{80-100i +56 i+70}{64 + 100} = \frac{150-44i }{164} = \frac{75}{82} + \frac{-11}{41}i \)
5. \((8+8i)\cdot (-9i)= -72 i-72i^2 = \color{red}{72}\color{blue}{-72i}\)
6. \((-10+8i) \cdot (-5-9i)= 50+90i -40 i-72i^2 = 50+90i -40 i+72= \color{red}{50+72}\color{blue}{+90i -40i}=\color{red}{122}\color{blue}{+50i}\)
7. \((3-10i) \cdot (-10-5i)= -30-15i +100 i+50i^2 = -30-15i +100 i-50= \color{red}{-30-50}\color{blue}{-15i +100i}=\color{red}{-80}\color{blue}{+85i}\)
8. \(\frac{-2+10i}{-7+2i}= \frac{-2+10i}{-7+2i} \cdot \frac{-7-2i}{-7-2i} = \frac{14+4i -70 i-20i^2 }{(-7)^2-(2i)^2} = \frac{14+4i -70 i+20}{49 + 4} = \frac{34-66i }{53} = \frac{34}{53} + \frac{-66}{53}i \)
9. \(\frac{-9+3i}{3+5i}= \frac{-9+3i}{3+5i} \cdot \frac{3-5i}{3-5i} = \frac{-27+45i +9 i-15i^2 }{(3)^2-(5i)^2} = \frac{-27+45i +9 i+15}{9 + 25} = \frac{-12+54i }{34} = \frac{-6}{17} - \frac{-27}{17}i \)
10. \((-7+10i) \cdot (10-10i)= -70+70i +100 i-100i^2 = -70+70i +100 i+100= \color{red}{-70+100}\color{blue}{+70i +100i}=\color{red}{30}\color{blue}{+170i}\)
11. \((3+4i) \cdot (-8+3i)= -24+9i -32 i+12i^2 = -24+9i -32 i-12= \color{red}{-24-12}\color{blue}{+9i -32i}=\color{red}{-36}\color{blue}{-23i}\)
12. \(\frac{3+6i}{-1+4i}= \frac{3+6i}{-1+4i} \cdot \frac{-1-4i}{-1-4i} = \frac{-3-12i -6 i-24i^2 }{(-1)^2-(4i)^2} = \frac{-3-12i -6 i+24}{1 + 16} = \frac{21-18i }{17} = \frac{21}{17} + \frac{-18}{17}i \)