Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{9+9i}{7-10i}= \frac{9+9i}{7-10i} \cdot \frac{7+10i}{7+10i} = \frac{63+90i +63 i+90i^2 }{(7)^2-(-10i)^2} = \frac{63+90i +63 i-90}{49 + 100} = \frac{-27+153i }{149} = \frac{-27}{149} - \frac{-153}{149}i \)
2. \((7-10i)-(5-i)= 7-10i -5+i =\color{red}{7-5}\color{blue}{-10i +i}=\color{red}{2}\color{blue}{-9i}\)
3. \(\frac{2+4i}{5-7i}= \frac{2+4i}{5-7i} \cdot \frac{5+7i}{5+7i} = \frac{10+14i +20 i+28i^2 }{(5)^2-(-7i)^2} = \frac{10+14i +20 i-28}{25 + 49} = \frac{-18+34i }{74} = \frac{-9}{37} - \frac{-17}{37}i \)
4. \((10-4i)-(5-10i)= 10-4i -5+10i =\color{red}{10-5}\color{blue}{-4i +10i}=\color{red}{5}\color{blue}{+6i}\)
5. \((9-2i)+(9+5i)= 9-2i +9+5i =\color{red}{9+9}\color{blue}{-2i +5i}=\color{red}{18}\color{blue}{+3i}\)
6. \((3+5i)\cdot (+5i)= +15 i+25i^2 = \color{red}{-25}\color{blue}{+15i}\)
7. \((-10-4i)+(-9-2i)= -10-4i -9-2i =\color{red}{-10-9}\color{blue}{-4i -2i}=\color{red}{-19}\color{blue}{-6i}\)
8. \((10-9i)-(-9-3i)= 10-9i +9+3i =\color{red}{10+9}\color{blue}{-9i +3i}=\color{red}{19}\color{blue}{-6i}\)
9. \((-5-7i)-(7-5i)= -5-7i -7+5i =\color{red}{-5-7}\color{blue}{-7i +5i}=\color{red}{-12}\color{blue}{-2i}\)
10. \(\frac{5-7i}{-10-9i}= \frac{5-7i}{-10-9i} \cdot \frac{-10+9i}{-10+9i} = \frac{-50+45i +70 i-63i^2 }{(-10)^2-(-9i)^2} = \frac{-50+45i +70 i+63}{100 + 81} = \frac{13+115i }{181} = \frac{13}{181} - \frac{-115}{181}i \)
11. \((6+3i)\cdot (-9i)= -54 i-27i^2 = \color{red}{27}\color{blue}{-54i}\)
12. \((+5i) \cdot (2-2i)= +10 i-10i^2 = \color{red}{10}\color{blue}{+10i}\)