Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9-7i)-(-7+3i)= -9-7i +7-3i =\color{red}{-9+7}\color{blue}{-7i -3i}=\color{red}{-2}\color{blue}{-10i}\)
2. \((4+7i)-(-3-6i)= 4+7i +3+6i =\color{red}{4+3}\color{blue}{+7i +6i}=\color{red}{7}\color{blue}{+13i}\)
3. \(\frac{-9-8i}{-2+8i}= \frac{-9-8i}{-2+8i} \cdot \frac{-2-8i}{-2-8i} = \frac{18+72i +16 i+64i^2 }{(-2)^2-(8i)^2} = \frac{18+72i +16 i-64}{4 + 64} = \frac{-46+88i }{68} = \frac{-23}{34} - \frac{-22}{17}i \)
4. \((6+i) \cdot (-9+8i)= -54+48i -9 i+8i^2 = -54+48i -9 i-8= \color{red}{-54-8}\color{blue}{+48i -9i}=\color{red}{-62}\color{blue}{+39i}\)
5. \((-4+i)+(4+2i)= -4+i +4+2i =\color{red}{-4+4}\color{blue}{+i +2i}=\color{blue}{3i}\)
6. \((2+6i) \cdot (6-4i)= 12-8i +36 i-24i^2 = 12-8i +36 i+24= \color{red}{12+24}\color{blue}{-8i +36i}=\color{red}{36}\color{blue}{+28i}\)
7. \((-8+8i)-(1+9i)= -8+8i -1-9i =\color{red}{-8-1}\color{blue}{+8i -9i}=\color{red}{-9}\color{blue}{-i}\)
8. \(\frac{-7+4i}{-1-9i}= \frac{-7+4i}{-1-9i} \cdot \frac{-1+9i}{-1+9i} = \frac{7-63i -4 i+36i^2 }{(-1)^2-(-9i)^2} = \frac{7-63i -4 i-36}{1 + 81} = \frac{-29-67i }{82} = \frac{-29}{82} + \frac{-67}{82}i \)
9. \((10-10i)\cdot (-5i)= -50 i+50i^2 = \color{red}{-50}\color{blue}{-50i}\)
10. \((-3+4i) \cdot (-1-10i)= 3+30i -4 i-40i^2 = 3+30i -4 i+40= \color{red}{3+40}\color{blue}{+30i -4i}=\color{red}{43}\color{blue}{+26i}\)
11. \((-2i) \cdot (-3+7i)= +6 i-14i^2 = \color{red}{14}\color{blue}{+6i}\)
12. \((-10+10i)+(7-10i)= -10+10i +7-10i =\color{red}{-10+7}\color{blue}{+10i -10i}=\color{red}{-3}\)