Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1+2i)+(3+10i)= -1+2i +3+10i =\color{red}{-1+3}\color{blue}{+2i +10i}=\color{red}{2}\color{blue}{+12i}\)
2. \((-5-9i)+(6+9i)= -5-9i +6+9i =\color{red}{-5+6}\color{blue}{-9i +9i}=\color{red}{1}\)
3. \((8-i) \cdot (-8+5i)= -64+40i +8 i-5i^2 = -64+40i +8 i+5= \color{red}{-64+5}\color{blue}{+40i +8i}=\color{red}{-59}\color{blue}{+48i}\)
4. \((8-i) \cdot (9+5i)= 72+40i -9 i-5i^2 = 72+40i -9 i+5= \color{red}{72+5}\color{blue}{+40i -9i}=\color{red}{77}\color{blue}{+31i}\)
5. \(\frac{10+9i}{-4-6i}= \frac{10+9i}{-4-6i} \cdot \frac{-4+6i}{-4+6i} = \frac{-40+60i -36 i+54i^2 }{(-4)^2-(-6i)^2} = \frac{-40+60i -36 i-54}{16 + 36} = \frac{-94+24i }{52} = \frac{-47}{26} - \frac{-6}{13}i \)
6. \(\frac{6-6i}{-8+7i}= \frac{6-6i}{-8+7i} \cdot \frac{-8-7i}{-8-7i} = \frac{-48-42i +48 i+42i^2 }{(-8)^2-(7i)^2} = \frac{-48-42i +48 i-42}{64 + 49} = \frac{-90+6i }{113} = \frac{-90}{113} - \frac{-6}{113}i \)
7. \(\frac{-10+3i}{1+6i}= \frac{-10+3i}{1+6i} \cdot \frac{1-6i}{1-6i} = \frac{-10+60i +3 i-18i^2 }{(1)^2-(6i)^2} = \frac{-10+60i +3 i+18}{1 + 36} = \frac{8+63i }{37} = \frac{8}{37} - \frac{-63}{37}i \)
8. \((-5-9i) \cdot (-5+7i)= 25-35i +45 i-63i^2 = 25-35i +45 i+63= \color{red}{25+63}\color{blue}{-35i +45i}=\color{red}{88}\color{blue}{+10i}\)
9. \((-5-3i)+(4+3i)= -5-3i +4+3i =\color{red}{-5+4}\color{blue}{-3i +3i}=\color{red}{-1}\)
10. \((10+2i) \cdot (1+4i)= 10+40i +2 i+8i^2 = 10+40i +2 i-8= \color{red}{10-8}\color{blue}{+40i +2i}=\color{red}{2}\color{blue}{+42i}\)
11. \((1+3i) \cdot (2+i)= 2+i +6 i+3i^2 = 2+i +6 i-3= \color{red}{2-3}\color{blue}{+i +6i}=\color{red}{-1}\color{blue}{+7i}\)
12. \((-10i) \cdot (6-6i)= -60 i+60i^2 = \color{red}{-60}\color{blue}{-60i}\)