Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5+7i) \cdot (10+2i)= 50+10i +70 i+14i^2 = 50+10i +70 i-14= \color{red}{50-14}\color{blue}{+10i +70i}=\color{red}{36}\color{blue}{+80i}\)
2. \((7-3i) \cdot (-7+2i)= -49+14i +21 i-6i^2 = -49+14i +21 i+6= \color{red}{-49+6}\color{blue}{+14i +21i}=\color{red}{-43}\color{blue}{+35i}\)
3. \((-2i) \cdot (-5-i)= +10 i+2i^2 = \color{red}{-2}\color{blue}{+10i}\)
4. \(\frac{5+9i}{-7-9i}= \frac{5+9i}{-7-9i} \cdot \frac{-7+9i}{-7+9i} = \frac{-35+45i -63 i+81i^2 }{(-7)^2-(-9i)^2} = \frac{-35+45i -63 i-81}{49 + 81} = \frac{-116-18i }{130} = \frac{-58}{65} + \frac{-9}{65}i \)
5. \((-8+9i)-(9+5i)= -8+9i -9-5i =\color{red}{-8-9}\color{blue}{+9i -5i}=\color{red}{-17}\color{blue}{+4i}\)
6. \((4-10i)+(5-4i)= 4-10i +5-4i =\color{red}{4+5}\color{blue}{-10i -4i}=\color{red}{9}\color{blue}{-14i}\)
7. \((4-8i) \cdot (8-5i)= 32-20i -64 i+40i^2 = 32-20i -64 i-40= \color{red}{32-40}\color{blue}{-20i -64i}=\color{red}{-8}\color{blue}{-84i}\)
8. \(\frac{10-4i}{3+2i}= \frac{10-4i}{3+2i} \cdot \frac{3-2i}{3-2i} = \frac{30-20i -12 i+8i^2 }{(3)^2-(2i)^2} = \frac{30-20i -12 i-8}{9 + 4} = \frac{22-32i }{13} = \frac{22}{13} + \frac{-32}{13}i \)
9. \((+4i) \cdot (-4-4i)= -16 i-16i^2 = \color{red}{16}\color{blue}{-16i}\)
10. \((-4-2i)+(10-8i)= -4-2i +10-8i =\color{red}{-4+10}\color{blue}{-2i -8i}=\color{red}{6}\color{blue}{-10i}\)
11. \((-3-5i)+(-1-i)= -3-5i -1-i =\color{red}{-3-1}\color{blue}{-5i -i}=\color{red}{-4}\color{blue}{-6i}\)
12. \((+4i) \cdot (-1+i)= -4 i+4i^2 = \color{red}{-4}\color{blue}{-4i}\)