Vermenigvuldigen en delen (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5+6i) \cdot (1-5i)= -5+25i +6 i-30i^2 = -5+25i +6 i+30= \color{red}{-5+30}\color{blue}{+25i +6i}=\color{red}{25}\color{blue}{+31i}\)
2. \(\frac{4+6i}{3-5i}= \frac{4+6i}{3-5i} \cdot \frac{3+5i}{3+5i} = \frac{12+20i +18 i+30i^2 }{(3)^2-(-5i)^2} = \frac{12+20i +18 i-30}{9 + 25} = \frac{-18+38i }{34} = \frac{-9}{17} - \frac{-19}{17}i \)
3. \(\frac{7+5i}{-10-6i}= \frac{7+5i}{-10-6i} \cdot \frac{-10+6i}{-10+6i} = \frac{-70+42i -50 i+30i^2 }{(-10)^2-(-6i)^2} = \frac{-70+42i -50 i-30}{100 + 36} = \frac{-100-8i }{136} = \frac{-25}{34} + \frac{-1}{17}i \)
4. \((5-6i) \cdot (5-10i)= 25-50i -30 i+60i^2 = 25-50i -30 i-60= \color{red}{25-60}\color{blue}{-50i -30i}=\color{red}{-35}\color{blue}{-80i}\)
5. \(\frac{5+8i}{8+4i}= \frac{5+8i}{8+4i} \cdot \frac{8-4i}{8-4i} = \frac{40-20i +64 i-32i^2 }{(8)^2-(4i)^2} = \frac{40-20i +64 i+32}{64 + 16} = \frac{72+44i }{80} = \frac{9}{10} - \frac{-11}{20}i \)
6. \((8-3i)\cdot (-10i)= -80 i+30i^2 = \color{red}{-30}\color{blue}{-80i}\)
7. \((8+3i) \cdot (-2+8i)= -16+64i -6 i+24i^2 = -16+64i -6 i-24= \color{red}{-16-24}\color{blue}{+64i -6i}=\color{red}{-40}\color{blue}{+58i}\)
8. \((-8+8i)\cdot (+9i)= -72 i+72i^2 = \color{red}{-72}\color{blue}{-72i}\)
9. \((-7i) \cdot (-3-4i)= +21 i+28i^2 = \color{red}{-28}\color{blue}{+21i}\)
10. \((4-4i) \cdot (-3-6i)= -12-24i +12 i+24i^2 = -12-24i +12 i-24= \color{red}{-12-24}\color{blue}{-24i +12i}=\color{red}{-36}\color{blue}{-12i}\)
11. \((9+2i) \cdot (-4-8i)= -36-72i -8 i-16i^2 = -36-72i -8 i+16= \color{red}{-36+16}\color{blue}{-72i -8i}=\color{red}{-20}\color{blue}{-80i}\)
12. \((-6-i) \cdot (6-i)= -36+6i -6 i+i^2 = -36+6i -6 i-= \color{red}{-36-1}\color{blue}{+6i -6i}=\color{red}{-37}\)