Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7+6i) \cdot (5-2i)= 35-14i +30 i-12i^2 = 35-14i +30 i+12= \color{red}{35+12}\color{blue}{-14i +30i}=\color{red}{47}\color{blue}{+16i}\)
2. \((9-6i) \cdot (-4+2i)= -36+18i +24 i-12i^2 = -36+18i +24 i+12= \color{red}{-36+12}\color{blue}{+18i +24i}=\color{red}{-24}\color{blue}{+42i}\)
3. \((-9+5i)\cdot (-9i)= +81 i-45i^2 = \color{red}{45}\color{blue}{+81i}\)
4. \((-6+i)-(1+4i)= -6+i -1-4i =\color{red}{-6-1}\color{blue}{+i -4i}=\color{red}{-7}\color{blue}{-3i}\)
5. \((-6i) \cdot (-8-3i)= +48 i+18i^2 = \color{red}{-18}\color{blue}{+48i}\)
6. \((3+9i)-(5-5i)= 3+9i -5+5i =\color{red}{3-5}\color{blue}{+9i +5i}=\color{red}{-2}\color{blue}{+14i}\)
7. \(\frac{4-5i}{3+8i}= \frac{4-5i}{3+8i} \cdot \frac{3-8i}{3-8i} = \frac{12-32i -15 i+40i^2 }{(3)^2-(8i)^2} = \frac{12-32i -15 i-40}{9 + 64} = \frac{-28-47i }{73} = \frac{-28}{73} + \frac{-47}{73}i \)
8. \((-9-8i)+(-1-i)= -9-8i -1-i =\color{red}{-9-1}\color{blue}{-8i -i}=\color{red}{-10}\color{blue}{-9i}\)
9. \((10+5i)\cdot (+5i)= +50 i+25i^2 = \color{red}{-25}\color{blue}{+50i}\)
10. \((8+4i)+(2-5i)= 8+4i +2-5i =\color{red}{8+2}\color{blue}{+4i -5i}=\color{red}{10}\color{blue}{-i}\)
11. \(\frac{8+6i}{10-2i}= \frac{8+6i}{10-2i} \cdot \frac{10+2i}{10+2i} = \frac{80+16i +60 i+12i^2 }{(10)^2-(-2i)^2} = \frac{80+16i +60 i-12}{100 + 4} = \frac{68+76i }{104} = \frac{17}{26} - \frac{-19}{26}i \)
12. \((-8-7i) \cdot (-4-9i)= 32+72i +28 i+63i^2 = 32+72i +28 i-63= \color{red}{32-63}\color{blue}{+72i +28i}=\color{red}{-31}\color{blue}{+100i}\)