Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((2+5i)+(5-3i)= 2+5i +5-3i =\color{red}{2+5}\color{blue}{+5i -3i}=\color{red}{7}\color{blue}{+2i}\)
2. \(\frac{5-7i}{-8-4i}= \frac{5-7i}{-8-4i} \cdot \frac{-8+4i}{-8+4i} = \frac{-40+20i +56 i-28i^2 }{(-8)^2-(-4i)^2} = \frac{-40+20i +56 i+28}{64 + 16} = \frac{-12+76i }{80} = \frac{-3}{20} - \frac{-19}{20}i \)
3. \((-4i) \cdot (-6-8i)= +24 i+32i^2 = \color{red}{-32}\color{blue}{+24i}\)
4. \((-2-8i)\cdot (-9i)= +18 i+72i^2 = \color{red}{-72}\color{blue}{+18i}\)
5. \((5+8i)+(-6-3i)= 5+8i -6-3i =\color{red}{5-6}\color{blue}{+8i -3i}=\color{red}{-1}\color{blue}{+5i}\)
6. \((-3+8i)+(4+5i)= -3+8i +4+5i =\color{red}{-3+4}\color{blue}{+8i +5i}=\color{red}{1}\color{blue}{+13i}\)
7. \((+7i) \cdot (7-10i)= +49 i-70i^2 = \color{red}{70}\color{blue}{+49i}\)
8. \((-1+5i)-(2-8i)= -1+5i -2+8i =\color{red}{-1-2}\color{blue}{+5i +8i}=\color{red}{-3}\color{blue}{+13i}\)
9. \(\frac{8+i}{-10+8i}= \frac{8+i}{-10+8i} \cdot \frac{-10-8i}{-10-8i} = \frac{-80-64i -10 i-8i^2 }{(-10)^2-(8i)^2} = \frac{-80-64i -10 i+8}{100 + 64} = \frac{-72-74i }{164} = \frac{-18}{41} + \frac{-37}{82}i \)
10. \(\frac{-6-5i}{-3+10i}= \frac{-6-5i}{-3+10i} \cdot \frac{-3-10i}{-3-10i} = \frac{18+60i +15 i+50i^2 }{(-3)^2-(10i)^2} = \frac{18+60i +15 i-50}{9 + 100} = \frac{-32+75i }{109} = \frac{-32}{109} - \frac{-75}{109}i \)
11. \((5-8i)+(2+4i)= 5-8i +2+4i =\color{red}{5+2}\color{blue}{-8i +4i}=\color{red}{7}\color{blue}{-4i}\)
12. \((+7i) \cdot (-9-8i)= -63 i-56i^2 = \color{red}{56}\color{blue}{-63i}\)