Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((3-7i) \cdot (-6+4i)= -18+12i +42 i-28i^2 = -18+12i +42 i+28= \color{red}{-18+28}\color{blue}{+12i +42i}=\color{red}{10}\color{blue}{+54i}\)
2. \((-4-4i) \cdot (9-8i)= -36+32i -36 i+32i^2 = -36+32i -36 i-32= \color{red}{-36-32}\color{blue}{+32i -36i}=\color{red}{-68}\color{blue}{-4i}\)
3. \((10+9i) \cdot (5+10i)= 50+100i +45 i+90i^2 = 50+100i +45 i-90= \color{red}{50-90}\color{blue}{+100i +45i}=\color{red}{-40}\color{blue}{+145i}\)
4. \((-5-3i)-(-9-i)= -5-3i +9+i =\color{red}{-5+9}\color{blue}{-3i +i}=\color{red}{4}\color{blue}{-2i}\)
5. \((-4+9i) \cdot (-1+9i)= 4-36i -9 i+81i^2 = 4-36i -9 i-81= \color{red}{4-81}\color{blue}{-36i -9i}=\color{red}{-77}\color{blue}{-45i}\)
6. \((3-7i) \cdot (2+5i)= 6+15i -14 i-35i^2 = 6+15i -14 i+35= \color{red}{6+35}\color{blue}{+15i -14i}=\color{red}{41}\color{blue}{+i}\)
7. \((-3+4i)+(2-3i)= -3+4i +2-3i =\color{red}{-3+2}\color{blue}{+4i -3i}=\color{red}{-1}\color{blue}{+i}\)
8. \((6+4i)-(4+9i)= 6+4i -4-9i =\color{red}{6-4}\color{blue}{+4i -9i}=\color{red}{2}\color{blue}{-5i}\)
9. \((3+10i)+(-3-i)= 3+10i -3-i =\color{red}{3-3}\color{blue}{+10i -i}=\color{blue}{9i}\)
10. \((4+9i)\cdot (+3i)= +12 i+27i^2 = \color{red}{-27}\color{blue}{+12i}\)
11. \(\frac{8+2i}{-10+7i}= \frac{8+2i}{-10+7i} \cdot \frac{-10-7i}{-10-7i} = \frac{-80-56i -20 i-14i^2 }{(-10)^2-(7i)^2} = \frac{-80-56i -20 i+14}{100 + 49} = \frac{-66-76i }{149} = \frac{-66}{149} + \frac{-76}{149}i \)
12. \((3-7i)\cdot (+7i)= +21 i-49i^2 = \color{red}{49}\color{blue}{+21i}\)