Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9-4i) \cdot (5-8i)= -45+72i -20 i+32i^2 = -45+72i -20 i-32= \color{red}{-45-32}\color{blue}{+72i -20i}=\color{red}{-77}\color{blue}{+52i}\)
2. \(\frac{-6+10i}{-2+5i}= \frac{-6+10i}{-2+5i} \cdot \frac{-2-5i}{-2-5i} = \frac{12+30i -20 i-50i^2 }{(-2)^2-(5i)^2} = \frac{12+30i -20 i+50}{4 + 25} = \frac{62+10i }{29} = \frac{62}{29} - \frac{-10}{29}i \)
3. \(\frac{-10-i}{-10+i}= \frac{-10-i}{-10+i} \cdot \frac{-10-i}{-10-i} = \frac{100+10i +10 i+i^2 }{(-10)^2-(1i)^2} = \frac{100+10i +10 i-}{100 + 1} = \frac{99+20i }{101} = \frac{99}{101} - \frac{-20}{101}i \)
4. \((2+4i) \cdot (7+9i)= 14+18i +28 i+36i^2 = 14+18i +28 i-36= \color{red}{14-36}\color{blue}{+18i +28i}=\color{red}{-22}\color{blue}{+46i}\)
5. \((8-2i) \cdot (10+i)= 80+8i -20 i-2i^2 = 80+8i -20 i+2= \color{red}{80+2}\color{blue}{+8i -20i}=\color{red}{82}\color{blue}{-12i}\)
6. \((-2i) \cdot (-3+7i)= +6 i-14i^2 = \color{red}{14}\color{blue}{+6i}\)
7. \(\frac{-5+2i}{-10+9i}= \frac{-5+2i}{-10+9i} \cdot \frac{-10-9i}{-10-9i} = \frac{50+45i -20 i-18i^2 }{(-10)^2-(9i)^2} = \frac{50+45i -20 i+18}{100 + 81} = \frac{68+25i }{181} = \frac{68}{181} - \frac{-25}{181}i \)
8. \((-4+6i)\cdot (+9i)= -36 i+54i^2 = \color{red}{-54}\color{blue}{-36i}\)
9. \((-8-2i) \cdot (-2-10i)= 16+80i +4 i+20i^2 = 16+80i +4 i-20= \color{red}{16-20}\color{blue}{+80i +4i}=\color{red}{-4}\color{blue}{+84i}\)
10. \(\frac{-1+6i}{2-3i}= \frac{-1+6i}{2-3i} \cdot \frac{2+3i}{2+3i} = \frac{-2-3i +12 i+18i^2 }{(2)^2-(-3i)^2} = \frac{-2-3i +12 i-18}{4 + 9} = \frac{-20+9i }{13} = \frac{-20}{13} - \frac{-9}{13}i \)
11. \((-6-i) \cdot (7-5i)= -42+30i -7 i+5i^2 = -42+30i -7 i-5= \color{red}{-42-5}\color{blue}{+30i -7i}=\color{red}{-47}\color{blue}{+23i}\)
12. \((-3i) \cdot (6-3i)= -18 i+9i^2 = \color{red}{-9}\color{blue}{-18i}\)