Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-8-9i) \cdot (10+9i)= -80-72i -90 i-81i^2 = -80-72i -90 i+81= \color{red}{-80+81}\color{blue}{-72i -90i}=\color{red}{1}\color{blue}{-162i}\)
2. \((6+i) \cdot (-6-7i)= -36-42i -6 i-7i^2 = -36-42i -6 i+7= \color{red}{-36+7}\color{blue}{-42i -6i}=\color{red}{-29}\color{blue}{-48i}\)
3. \((6-7i)\cdot (-10i)= -60 i+70i^2 = \color{red}{-70}\color{blue}{-60i}\)
4. \((2-3i)\cdot (+7i)= +14 i-21i^2 = \color{red}{21}\color{blue}{+14i}\)
5. \((2-5i)+(-8-i)= 2-5i -8-i =\color{red}{2-8}\color{blue}{-5i -i}=\color{red}{-6}\color{blue}{-6i}\)
6. \((-3i) \cdot (3+10i)= -9 i-30i^2 = \color{red}{30}\color{blue}{-9i}\)
7. \((-7-4i)\cdot (-9i)= +63 i+36i^2 = \color{red}{-36}\color{blue}{+63i}\)
8. \((3-7i) \cdot (-6+2i)= -18+6i +42 i-14i^2 = -18+6i +42 i+14= \color{red}{-18+14}\color{blue}{+6i +42i}=\color{red}{-4}\color{blue}{+48i}\)
9. \(\frac{-7-10i}{-8-4i}= \frac{-7-10i}{-8-4i} \cdot \frac{-8+4i}{-8+4i} = \frac{56-28i +80 i-40i^2 }{(-8)^2-(-4i)^2} = \frac{56-28i +80 i+40}{64 + 16} = \frac{96+52i }{80} = \frac{6}{5} - \frac{-13}{20}i \)
10. \((-10+9i)\cdot (-8i)= +80 i-72i^2 = \color{red}{72}\color{blue}{+80i}\)
11. \((-i) \cdot (5+2i)= -5 i-2i^2 = \color{red}{2}\color{blue}{-5i}\)
12. \((-10+4i)-(3-i)= -10+4i -3+i =\color{red}{-10-3}\color{blue}{+4i +i}=\color{red}{-13}\color{blue}{+5i}\)