Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7+10i) \cdot (7+3i)= -49-21i +70 i+30i^2 = -49-21i +70 i-30= \color{red}{-49-30}\color{blue}{-21i +70i}=\color{red}{-79}\color{blue}{+49i}\)
2. \(\frac{8+6i}{-2-6i}= \frac{8+6i}{-2-6i} \cdot \frac{-2+6i}{-2+6i} = \frac{-16+48i -12 i+36i^2 }{(-2)^2-(-6i)^2} = \frac{-16+48i -12 i-36}{4 + 36} = \frac{-52+36i }{40} = \frac{-13}{10} - \frac{-9}{10}i \)
3. \(\frac{-3+6i}{-9+4i}= \frac{-3+6i}{-9+4i} \cdot \frac{-9-4i}{-9-4i} = \frac{27+12i -54 i-24i^2 }{(-9)^2-(4i)^2} = \frac{27+12i -54 i+24}{81 + 16} = \frac{51-42i }{97} = \frac{51}{97} + \frac{-42}{97}i \)
4. \((-10+i) \cdot (-6+5i)= 60-50i -6 i+5i^2 = 60-50i -6 i-5= \color{red}{60-5}\color{blue}{-50i -6i}=\color{red}{55}\color{blue}{-56i}\)
5. \((7-2i)\cdot (-4i)= -28 i+8i^2 = \color{red}{-8}\color{blue}{-28i}\)
6. \((-9+4i)+(-4-9i)= -9+4i -4-9i =\color{red}{-9-4}\color{blue}{+4i -9i}=\color{red}{-13}\color{blue}{-5i}\)
7. \((10-i) \cdot (1-4i)= 10-40i -1 i+4i^2 = 10-40i -1 i-4= \color{red}{10-4}\color{blue}{-40i -i}=\color{red}{6}\color{blue}{-41i}\)
8. \((-3-i)\cdot (-4i)= +12 i+4i^2 = \color{red}{-4}\color{blue}{+12i}\)
9. \((2-3i)\cdot (-5i)= -10 i+15i^2 = \color{red}{-15}\color{blue}{-10i}\)
10. \((1-i)-(-4+4i)= 1-i +4-4i =\color{red}{1+4}\color{blue}{-i -4i}=\color{red}{5}\color{blue}{-5i}\)
11. \((-3+2i)-(6-i)= -3+2i -6+i =\color{red}{-3-6}\color{blue}{+2i +i}=\color{red}{-9}\color{blue}{+3i}\)
12. \((-6i) \cdot (-9-7i)= +54 i+42i^2 = \color{red}{-42}\color{blue}{+54i}\)