Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-7+i}{7+5i}= \frac{-7+i}{7+5i} \cdot \frac{7-5i}{7-5i} = \frac{-49+35i +7 i-5i^2 }{(7)^2-(5i)^2} = \frac{-49+35i +7 i+5}{49 + 25} = \frac{-44+42i }{74} = \frac{-22}{37} - \frac{-21}{37}i \)
2. \((2+10i)+(-2+i)= 2+10i -2+i =\color{red}{2-2}\color{blue}{+10i +i}=\color{blue}{11i}\)
3. \((-10i) \cdot (8+4i)= -80 i-40i^2 = \color{red}{40}\color{blue}{-80i}\)
4. \((8-10i)-(-1-2i)= 8-10i +1+2i =\color{red}{8+1}\color{blue}{-10i +2i}=\color{red}{9}\color{blue}{-8i}\)
5. \((-6+3i)-(-7+4i)= -6+3i +7-4i =\color{red}{-6+7}\color{blue}{+3i -4i}=\color{red}{1}\color{blue}{-i}\)
6. \((2+3i)\cdot (-9i)= -18 i-27i^2 = \color{red}{27}\color{blue}{-18i}\)
7. \((1-3i) \cdot (-9+3i)= -9+3i +27 i-9i^2 = -9+3i +27 i+9= \color{red}{-9+9}\color{blue}{+3i +27i}=\color{blue}{30i}\)
8. \((3+4i)+(9+3i)= 3+4i +9+3i =\color{red}{3+9}\color{blue}{+4i +3i}=\color{red}{12}\color{blue}{+7i}\)
9. \((7+5i) \cdot (3-8i)= 21-56i +15 i-40i^2 = 21-56i +15 i+40= \color{red}{21+40}\color{blue}{-56i +15i}=\color{red}{61}\color{blue}{-41i}\)
10. \((2+7i)\cdot (-4i)= -8 i-28i^2 = \color{red}{28}\color{blue}{-8i}\)
11. \((1+8i)-(8+7i)= 1+8i -8-7i =\color{red}{1-8}\color{blue}{+8i -7i}=\color{red}{-7}\color{blue}{+i}\)
12. \((-10-i)\cdot (-5i)= +50 i+5i^2 = \color{red}{-5}\color{blue}{+50i}\)