Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+5i) \cdot (-6-6i)= -30 i-30i^2 = \color{red}{30}\color{blue}{-30i}\)
2. \(\frac{-2+10i}{-10+7i}= \frac{-2+10i}{-10+7i} \cdot \frac{-10-7i}{-10-7i} = \frac{20+14i -100 i-70i^2 }{(-10)^2-(7i)^2} = \frac{20+14i -100 i+70}{100 + 49} = \frac{90-86i }{149} = \frac{90}{149} + \frac{-86}{149}i \)
3. \(\frac{-9+9i}{-1-10i}= \frac{-9+9i}{-1-10i} \cdot \frac{-1+10i}{-1+10i} = \frac{9-90i -9 i+90i^2 }{(-1)^2-(-10i)^2} = \frac{9-90i -9 i-90}{1 + 100} = \frac{-81-99i }{101} = \frac{-81}{101} + \frac{-99}{101}i \)
4. \(\frac{10+5i}{7-2i}= \frac{10+5i}{7-2i} \cdot \frac{7+2i}{7+2i} = \frac{70+20i +35 i+10i^2 }{(7)^2-(-2i)^2} = \frac{70+20i +35 i-10}{49 + 4} = \frac{60+55i }{53} = \frac{60}{53} - \frac{-55}{53}i \)
5. \((2+7i) \cdot (3+9i)= 6+18i +21 i+63i^2 = 6+18i +21 i-63= \color{red}{6-63}\color{blue}{+18i +21i}=\color{red}{-57}\color{blue}{+39i}\)
6. \((-10+6i) \cdot (-6+6i)= 60-60i -36 i+36i^2 = 60-60i -36 i-36= \color{red}{60-36}\color{blue}{-60i -36i}=\color{red}{24}\color{blue}{-96i}\)
7. \(\frac{2+i}{2-i}= \frac{2+i}{2-i} \cdot \frac{2+i}{2+i} = \frac{4+2i +2 i+i^2 }{(2)^2-(-1i)^2} = \frac{4+2i +2 i-}{4 + 1} = \frac{3+4i }{5} = \frac{3}{5} - \frac{-4}{5}i \)
8. \(\frac{7+6i}{7+2i}= \frac{7+6i}{7+2i} \cdot \frac{7-2i}{7-2i} = \frac{49-14i +42 i-12i^2 }{(7)^2-(2i)^2} = \frac{49-14i +42 i+12}{49 + 4} = \frac{61+28i }{53} = \frac{61}{53} - \frac{-28}{53}i \)
9. \(\frac{-5-9i}{-9-10i}= \frac{-5-9i}{-9-10i} \cdot \frac{-9+10i}{-9+10i} = \frac{45-50i +81 i-90i^2 }{(-9)^2-(-10i)^2} = \frac{45-50i +81 i+90}{81 + 100} = \frac{135+31i }{181} = \frac{135}{181} - \frac{-31}{181}i \)
10. \((4-5i)\cdot (-10i)= -40 i+50i^2 = \color{red}{-50}\color{blue}{-40i}\)
11. \(\frac{-3-8i}{3+6i}= \frac{-3-8i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{-9+18i -24 i+48i^2 }{(3)^2-(6i)^2} = \frac{-9+18i -24 i-48}{9 + 36} = \frac{-57-6i }{45} = \frac{-19}{15} + \frac{-2}{15}i \)
12. \((+4i) \cdot (10+7i)= +40 i+28i^2 = \color{red}{-28}\color{blue}{+40i}\)