Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9-5i)\cdot (+10i)= +90 i-50i^2 = \color{red}{50}\color{blue}{+90i}\)
2. \((-1-8i)-(8+4i)= -1-8i -8-4i =\color{red}{-1-8}\color{blue}{-8i -4i}=\color{red}{-9}\color{blue}{-12i}\)
3. \(\frac{6-6i}{8-3i}= \frac{6-6i}{8-3i} \cdot \frac{8+3i}{8+3i} = \frac{48+18i -48 i-18i^2 }{(8)^2-(-3i)^2} = \frac{48+18i -48 i+18}{64 + 9} = \frac{66-30i }{73} = \frac{66}{73} + \frac{-30}{73}i \)
4. \((10-9i)+(-2+i)= 10-9i -2+i =\color{red}{10-2}\color{blue}{-9i +i}=\color{red}{8}\color{blue}{-8i}\)
5. \((-5+8i)-(-7+7i)= -5+8i +7-7i =\color{red}{-5+7}\color{blue}{+8i -7i}=\color{red}{2}\color{blue}{+i}\)
6. \(\frac{-7+4i}{5-9i}= \frac{-7+4i}{5-9i} \cdot \frac{5+9i}{5+9i} = \frac{-35-63i +20 i+36i^2 }{(5)^2-(-9i)^2} = \frac{-35-63i +20 i-36}{25 + 81} = \frac{-71-43i }{106} = \frac{-71}{106} + \frac{-43}{106}i \)
7. \((-8-9i) \cdot (1+3i)= -8-24i -9 i-27i^2 = -8-24i -9 i+27= \color{red}{-8+27}\color{blue}{-24i -9i}=\color{red}{19}\color{blue}{-33i}\)
8. \((-4-9i) \cdot (10-10i)= -40+40i -90 i+90i^2 = -40+40i -90 i-90= \color{red}{-40-90}\color{blue}{+40i -90i}=\color{red}{-130}\color{blue}{-50i}\)
9. \((10-5i)+(6+4i)= 10-5i +6+4i =\color{red}{10+6}\color{blue}{-5i +4i}=\color{red}{16}\color{blue}{-i}\)
10. \((1-5i) \cdot (9+9i)= 9+9i -45 i-45i^2 = 9+9i -45 i+45= \color{red}{9+45}\color{blue}{+9i -45i}=\color{red}{54}\color{blue}{-36i}\)
11. \((8-5i)+(-2-7i)= 8-5i -2-7i =\color{red}{8-2}\color{blue}{-5i -7i}=\color{red}{6}\color{blue}{-12i}\)
12. \((-9+i)+(-8+2i)= -9+i -8+2i =\color{red}{-9-8}\color{blue}{+i +2i}=\color{red}{-17}\color{blue}{+3i}\)