Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5-10i)-(1-5i)= 5-10i -1+5i =\color{red}{5-1}\color{blue}{-10i +5i}=\color{red}{4}\color{blue}{-5i}\)
2. \((+7i) \cdot (3-i)= +21 i-7i^2 = \color{red}{7}\color{blue}{+21i}\)
3. \(\frac{5-7i}{5-6i}= \frac{5-7i}{5-6i} \cdot \frac{5+6i}{5+6i} = \frac{25+30i -35 i-42i^2 }{(5)^2-(-6i)^2} = \frac{25+30i -35 i+42}{25 + 36} = \frac{67-5i }{61} = \frac{67}{61} + \frac{-5}{61}i \)
4. \((6-8i)+(-8-9i)= 6-8i -8-9i =\color{red}{6-8}\color{blue}{-8i -9i}=\color{red}{-2}\color{blue}{-17i}\)
5. \(\frac{4+4i}{9+9i}= \frac{4+4i}{9+9i} \cdot \frac{9-9i}{9-9i} = \frac{36-36i +36 i-36i^2 }{(9)^2-(9i)^2} = \frac{36-36i +36 i+36}{81 + 81} = \frac{72+0i }{162} = \frac{4}{9} + 0i\)
6. \(\frac{-10-8i}{-10+10i}= \frac{-10-8i}{-10+10i} \cdot \frac{-10-10i}{-10-10i} = \frac{100+100i +80 i+80i^2 }{(-10)^2-(10i)^2} = \frac{100+100i +80 i-80}{100 + 100} = \frac{20+180i }{200} = \frac{1}{10} - \frac{-9}{10}i \)
7. \((-2+2i) \cdot (7+2i)= -14-4i +14 i+4i^2 = -14-4i +14 i-4= \color{red}{-14-4}\color{blue}{-4i +14i}=\color{red}{-18}\color{blue}{+10i}\)
8. \((-8-3i)\cdot (+5i)= -40 i-15i^2 = \color{red}{15}\color{blue}{-40i}\)
9. \((-4+7i)-(6+3i)= -4+7i -6-3i =\color{red}{-4-6}\color{blue}{+7i -3i}=\color{red}{-10}\color{blue}{+4i}\)
10. \((-2-7i) \cdot (-4-5i)= 8+10i +28 i+35i^2 = 8+10i +28 i-35= \color{red}{8-35}\color{blue}{+10i +28i}=\color{red}{-27}\color{blue}{+38i}\)
11. \((1-5i)\cdot (-i)= -1 i+5i^2 = \color{red}{-5}\color{blue}{-i}\)
12. \(\frac{-7+6i}{-1+7i}= \frac{-7+6i}{-1+7i} \cdot \frac{-1-7i}{-1-7i} = \frac{7+49i -6 i-42i^2 }{(-1)^2-(7i)^2} = \frac{7+49i -6 i+42}{1 + 49} = \frac{49+43i }{50} = \frac{49}{50} - \frac{-43}{50}i \)