Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-2+10i) \cdot (3-3i)= -6+6i +30 i-30i^2 = -6+6i +30 i+30= \color{red}{-6+30}\color{blue}{+6i +30i}=\color{red}{24}\color{blue}{+36i}\)
2. \((+3i) \cdot (3-6i)= +9 i-18i^2 = \color{red}{18}\color{blue}{+9i}\)
3. \((-6i) \cdot (-8-6i)= +48 i+36i^2 = \color{red}{-36}\color{blue}{+48i}\)
4. \((-5-10i) \cdot (6+3i)= -30-15i -60 i-30i^2 = -30-15i -60 i+30= \color{red}{-30+30}\color{blue}{-15i -60i}=\color{blue}{-75i}\)
5. \((1-9i)\cdot (+9i)= +9 i-81i^2 = \color{red}{81}\color{blue}{+9i}\)
6. \((7-7i)\cdot (-8i)= -56 i+56i^2 = \color{red}{-56}\color{blue}{-56i}\)
7. \(\frac{2+9i}{-10-i}= \frac{2+9i}{-10-i} \cdot \frac{-10+i}{-10+i} = \frac{-20+2i -90 i+9i^2 }{(-10)^2-(-1i)^2} = \frac{-20+2i -90 i-9}{100 + 1} = \frac{-29-88i }{101} = \frac{-29}{101} + \frac{-88}{101}i \)
8. \(\frac{2-10i}{-8+2i}= \frac{2-10i}{-8+2i} \cdot \frac{-8-2i}{-8-2i} = \frac{-16-4i +80 i+20i^2 }{(-8)^2-(2i)^2} = \frac{-16-4i +80 i-20}{64 + 4} = \frac{-36+76i }{68} = \frac{-9}{17} - \frac{-19}{17}i \)
9. \((9-10i) \cdot (-5-7i)= -45-63i +50 i+70i^2 = -45-63i +50 i-70= \color{red}{-45-70}\color{blue}{-63i +50i}=\color{red}{-115}\color{blue}{-13i}\)
10. \((-3i) \cdot (1+10i)= -3 i-30i^2 = \color{red}{30}\color{blue}{-3i}\)
11. \((-9+8i)\cdot (-7i)= +63 i-56i^2 = \color{red}{56}\color{blue}{+63i}\)
12. \((3+4i)\cdot (-9i)= -27 i-36i^2 = \color{red}{36}\color{blue}{-27i}\)