Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5+9i)-(7+6i)= 5+9i -7-6i =\color{red}{5-7}\color{blue}{+9i -6i}=\color{red}{-2}\color{blue}{+3i}\)
2. \(\frac{4+5i}{-9-5i}= \frac{4+5i}{-9-5i} \cdot \frac{-9+5i}{-9+5i} = \frac{-36+20i -45 i+25i^2 }{(-9)^2-(-5i)^2} = \frac{-36+20i -45 i-25}{81 + 25} = \frac{-61-25i }{106} = \frac{-61}{106} + \frac{-25}{106}i \)
3. \((7+2i)\cdot (+4i)= +28 i+8i^2 = \color{red}{-8}\color{blue}{+28i}\)
4. \(\frac{-6+7i}{-2+9i}= \frac{-6+7i}{-2+9i} \cdot \frac{-2-9i}{-2-9i} = \frac{12+54i -14 i-63i^2 }{(-2)^2-(9i)^2} = \frac{12+54i -14 i+63}{4 + 81} = \frac{75+40i }{85} = \frac{15}{17} - \frac{-8}{17}i \)
5. \((-9i) \cdot (-1-i)= +9 i+9i^2 = \color{red}{-9}\color{blue}{+9i}\)
6. \(\frac{-2-9i}{-9-7i}= \frac{-2-9i}{-9-7i} \cdot \frac{-9+7i}{-9+7i} = \frac{18-14i +81 i-63i^2 }{(-9)^2-(-7i)^2} = \frac{18-14i +81 i+63}{81 + 49} = \frac{81+67i }{130} = \frac{81}{130} - \frac{-67}{130}i \)
7. \((9-6i) \cdot (-8+10i)= -72+90i +48 i-60i^2 = -72+90i +48 i+60= \color{red}{-72+60}\color{blue}{+90i +48i}=\color{red}{-12}\color{blue}{+138i}\)
8. \(\frac{-2+i}{5+7i}= \frac{-2+i}{5+7i} \cdot \frac{5-7i}{5-7i} = \frac{-10+14i +5 i-7i^2 }{(5)^2-(7i)^2} = \frac{-10+14i +5 i+7}{25 + 49} = \frac{-3+19i }{74} = \frac{-3}{74} - \frac{-19}{74}i \)
9. \((9+3i)-(4-i)= 9+3i -4+i =\color{red}{9-4}\color{blue}{+3i +i}=\color{red}{5}\color{blue}{+4i}\)
10. \((3+2i)+(6+8i)= 3+2i +6+8i =\color{red}{3+6}\color{blue}{+2i +8i}=\color{red}{9}\color{blue}{+10i}\)
11. \((-5-7i) \cdot (1-7i)= -5+35i -7 i+49i^2 = -5+35i -7 i-49= \color{red}{-5-49}\color{blue}{+35i -7i}=\color{red}{-54}\color{blue}{+28i}\)
12. \((8-4i)-(-2-3i)= 8-4i +2+3i =\color{red}{8+2}\color{blue}{-4i +3i}=\color{red}{10}\color{blue}{-i}\)