Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{8+6i}{1+9i}= \frac{8+6i}{1+9i} \cdot \frac{1-9i}{1-9i} = \frac{8-72i +6 i-54i^2 }{(1)^2-(9i)^2} = \frac{8-72i +6 i+54}{1 + 81} = \frac{62-66i }{82} = \frac{31}{41} + \frac{-33}{41}i \)
2. \((3-9i)+(10+10i)= 3-9i +10+10i =\color{red}{3+10}\color{blue}{-9i +10i}=\color{red}{13}\color{blue}{+i}\)
3. \((+10i) \cdot (-8+2i)= -80 i+20i^2 = \color{red}{-20}\color{blue}{-80i}\)
4. \((4-7i)+(10+i)= 4-7i +10+i =\color{red}{4+10}\color{blue}{-7i +i}=\color{red}{14}\color{blue}{-6i}\)
5. \((1-4i)+(10-9i)= 1-4i +10-9i =\color{red}{1+10}\color{blue}{-4i -9i}=\color{red}{11}\color{blue}{-13i}\)
6. \((3+6i) \cdot (9+2i)= 27+6i +54 i+12i^2 = 27+6i +54 i-12= \color{red}{27-12}\color{blue}{+6i +54i}=\color{red}{15}\color{blue}{+60i}\)
7. \((7+8i)+(8+10i)= 7+8i +8+10i =\color{red}{7+8}\color{blue}{+8i +10i}=\color{red}{15}\color{blue}{+18i}\)
8. \((-4-5i)-(10-8i)= -4-5i -10+8i =\color{red}{-4-10}\color{blue}{-5i +8i}=\color{red}{-14}\color{blue}{+3i}\)
9. \((-5+7i)+(4-5i)= -5+7i +4-5i =\color{red}{-5+4}\color{blue}{+7i -5i}=\color{red}{-1}\color{blue}{+2i}\)
10. \((-8+7i) \cdot (-7+8i)= 56-64i -49 i+56i^2 = 56-64i -49 i-56= \color{red}{56-56}\color{blue}{-64i -49i}=\color{blue}{-113i}\)
11. \((-10+10i)-(6-7i)= -10+10i -6+7i =\color{red}{-10-6}\color{blue}{+10i +7i}=\color{red}{-16}\color{blue}{+17i}\)
12. \(\frac{8+3i}{-4+i}= \frac{8+3i}{-4+i} \cdot \frac{-4-i}{-4-i} = \frac{-32-8i -12 i-3i^2 }{(-4)^2-(1i)^2} = \frac{-32-8i -12 i+3}{16 + 1} = \frac{-29-20i }{17} = \frac{-29}{17} + \frac{-20}{17}i \)