Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5i) \cdot (5+10i)= -25 i-50i^2 = \color{red}{50}\color{blue}{-25i}\)
2. \((9+10i)+(-9-8i)= 9+10i -9-8i =\color{red}{9-9}\color{blue}{+10i -8i}=\color{blue}{2i}\)
3. \(\frac{-7-8i}{10+8i}= \frac{-7-8i}{10+8i} \cdot \frac{10-8i}{10-8i} = \frac{-70+56i -80 i+64i^2 }{(10)^2-(8i)^2} = \frac{-70+56i -80 i-64}{100 + 64} = \frac{-134-24i }{164} = \frac{-67}{82} + \frac{-6}{41}i \)
4. \((-10-6i)-(8-9i)= -10-6i -8+9i =\color{red}{-10-8}\color{blue}{-6i +9i}=\color{red}{-18}\color{blue}{+3i}\)
5. \(\frac{9+8i}{-4-4i}= \frac{9+8i}{-4-4i} \cdot \frac{-4+4i}{-4+4i} = \frac{-36+36i -32 i+32i^2 }{(-4)^2-(-4i)^2} = \frac{-36+36i -32 i-32}{16 + 16} = \frac{-68+4i }{32} = \frac{-17}{8} - \frac{-1}{8}i \)
6. \((-2-2i)\cdot (-6i)= +12 i+12i^2 = \color{red}{-12}\color{blue}{+12i}\)
7. \((-1+10i) \cdot (-2+i)= 2-i -20 i+10i^2 = 2-i -20 i-10= \color{red}{2-10}\color{blue}{-i -20i}=\color{red}{-8}\color{blue}{-21i}\)
8. \(\frac{8-7i}{-5-2i}= \frac{8-7i}{-5-2i} \cdot \frac{-5+2i}{-5+2i} = \frac{-40+16i +35 i-14i^2 }{(-5)^2-(-2i)^2} = \frac{-40+16i +35 i+14}{25 + 4} = \frac{-26+51i }{29} = \frac{-26}{29} - \frac{-51}{29}i \)
9. \((2+7i)+(10+2i)= 2+7i +10+2i =\color{red}{2+10}\color{blue}{+7i +2i}=\color{red}{12}\color{blue}{+9i}\)
10. \((-2-5i)+(8-5i)= -2-5i +8-5i =\color{red}{-2+8}\color{blue}{-5i -5i}=\color{red}{6}\color{blue}{-10i}\)
11. \(\frac{-4+9i}{-9+2i}= \frac{-4+9i}{-9+2i} \cdot \frac{-9-2i}{-9-2i} = \frac{36+8i -81 i-18i^2 }{(-9)^2-(2i)^2} = \frac{36+8i -81 i+18}{81 + 4} = \frac{54-73i }{85} = \frac{54}{85} + \frac{-73}{85}i \)
12. \((-3i) \cdot (-4-3i)= +12 i+9i^2 = \color{red}{-9}\color{blue}{+12i}\)