Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1+8i)+(-7-6i)= -1+8i -7-6i =\color{red}{-1-7}\color{blue}{+8i -6i}=\color{red}{-8}\color{blue}{+2i}\)
2. \((10-2i)\cdot (-7i)= -70 i+14i^2 = \color{red}{-14}\color{blue}{-70i}\)
3. \(\frac{4-3i}{-9-10i}= \frac{4-3i}{-9-10i} \cdot \frac{-9+10i}{-9+10i} = \frac{-36+40i +27 i-30i^2 }{(-9)^2-(-10i)^2} = \frac{-36+40i +27 i+30}{81 + 100} = \frac{-6+67i }{181} = \frac{-6}{181} - \frac{-67}{181}i \)
4. \((-4+i)-(-1-9i)= -4+i +1+9i =\color{red}{-4+1}\color{blue}{+i +9i}=\color{red}{-3}\color{blue}{+10i}\)
5. \((9+4i)+(-9+8i)= 9+4i -9+8i =\color{red}{9-9}\color{blue}{+4i +8i}=\color{blue}{12i}\)
6. \((-10+i)-(-5-i)= -10+i +5+i =\color{red}{-10+5}\color{blue}{+i +i}=\color{red}{-5}\color{blue}{+2i}\)
7. \((-9i) \cdot (6-4i)= -54 i+36i^2 = \color{red}{-36}\color{blue}{-54i}\)
8. \(\frac{2+3i}{-10+8i}= \frac{2+3i}{-10+8i} \cdot \frac{-10-8i}{-10-8i} = \frac{-20-16i -30 i-24i^2 }{(-10)^2-(8i)^2} = \frac{-20-16i -30 i+24}{100 + 64} = \frac{4-46i }{164} = \frac{1}{41} + \frac{-23}{82}i \)
9. \((+4i) \cdot (-10-5i)= -40 i-20i^2 = \color{red}{20}\color{blue}{-40i}\)
10. \(\frac{2+i}{-3+8i}= \frac{2+i}{-3+8i} \cdot \frac{-3-8i}{-3-8i} = \frac{-6-16i -3 i-8i^2 }{(-3)^2-(8i)^2} = \frac{-6-16i -3 i+8}{9 + 64} = \frac{2-19i }{73} = \frac{2}{73} + \frac{-19}{73}i \)
11. \((-7-i)-(-7+3i)= -7-i +7-3i =\color{red}{-7+7}\color{blue}{-i -3i}=\color{blue}{-4i}\)
12. \((3+7i)\cdot (-6i)= -18 i-42i^2 = \color{red}{42}\color{blue}{-18i}\)