Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7-5i)+(-8+i)= 7-5i -8+i =\color{red}{7-8}\color{blue}{-5i +i}=\color{red}{-1}\color{blue}{-4i}\)
2. \((-2+4i)\cdot (-7i)= +14 i-28i^2 = \color{red}{28}\color{blue}{+14i}\)
3. \((2-10i) \cdot (-6+9i)= -12+18i +60 i-90i^2 = -12+18i +60 i+90= \color{red}{-12+90}\color{blue}{+18i +60i}=\color{red}{78}\color{blue}{+78i}\)
4. \((-9+6i)-(2+10i)= -9+6i -2-10i =\color{red}{-9-2}\color{blue}{+6i -10i}=\color{red}{-11}\color{blue}{-4i}\)
5. \((-9+7i)\cdot (+10i)= -90 i+70i^2 = \color{red}{-70}\color{blue}{-90i}\)
6. \((-10+3i) \cdot (5+9i)= -50-90i +15 i+27i^2 = -50-90i +15 i-27= \color{red}{-50-27}\color{blue}{-90i +15i}=\color{red}{-77}\color{blue}{-75i}\)
7. \((-5i) \cdot (-10+2i)= +50 i-10i^2 = \color{red}{10}\color{blue}{+50i}\)
8. \((-6-8i) \cdot (7+7i)= -42-42i -56 i-56i^2 = -42-42i -56 i+56= \color{red}{-42+56}\color{blue}{-42i -56i}=\color{red}{14}\color{blue}{-98i}\)
9. \((+10i) \cdot (-8+4i)= -80 i+40i^2 = \color{red}{-40}\color{blue}{-80i}\)
10. \((-9-9i)+(9-3i)= -9-9i +9-3i =\color{red}{-9+9}\color{blue}{-9i -3i}=\color{blue}{-12i}\)
11. \((-3+10i)-(9-10i)= -3+10i -9+10i =\color{red}{-3-9}\color{blue}{+10i +10i}=\color{red}{-12}\color{blue}{+20i}\)
12. \(\frac{-8+i}{4+8i}= \frac{-8+i}{4+8i} \cdot \frac{4-8i}{4-8i} = \frac{-32+64i +4 i-8i^2 }{(4)^2-(8i)^2} = \frac{-32+64i +4 i+8}{16 + 64} = \frac{-24+68i }{80} = \frac{-3}{10} - \frac{-17}{20}i \)