Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{8-4i}{5+2i}= \frac{8-4i}{5+2i} \cdot \frac{5-2i}{5-2i} = \frac{40-16i -20 i+8i^2 }{(5)^2-(2i)^2} = \frac{40-16i -20 i-8}{25 + 4} = \frac{32-36i }{29} = \frac{32}{29} + \frac{-36}{29}i \)
2. \((-10i) \cdot (-2+3i)= +20 i-30i^2 = \color{red}{30}\color{blue}{+20i}\)
3. \(\frac{7+4i}{-6-3i}= \frac{7+4i}{-6-3i} \cdot \frac{-6+3i}{-6+3i} = \frac{-42+21i -24 i+12i^2 }{(-6)^2-(-3i)^2} = \frac{-42+21i -24 i-12}{36 + 9} = \frac{-54-3i }{45} = \frac{-6}{5} + \frac{-1}{15}i \)
4. \((9+5i)-(2-8i)= 9+5i -2+8i =\color{red}{9-2}\color{blue}{+5i +8i}=\color{red}{7}\color{blue}{+13i}\)
5. \((2-10i) \cdot (-10+9i)= -20+18i +100 i-90i^2 = -20+18i +100 i+90= \color{red}{-20+90}\color{blue}{+18i +100i}=\color{red}{70}\color{blue}{+118i}\)
6. \((-2i) \cdot (-5-6i)= +10 i+12i^2 = \color{red}{-12}\color{blue}{+10i}\)
7. \((-1-8i)-(-2+7i)= -1-8i +2-7i =\color{red}{-1+2}\color{blue}{-8i -7i}=\color{red}{1}\color{blue}{-15i}\)
8. \((-3+i)\cdot (+6i)= -18 i+6i^2 = \color{red}{-6}\color{blue}{-18i}\)
9. \((-6+10i)\cdot (-i)= +6 i-10i^2 = \color{red}{10}\color{blue}{+6i}\)
10. \(\frac{-5-5i}{-8-10i}= \frac{-5-5i}{-8-10i} \cdot \frac{-8+10i}{-8+10i} = \frac{40-50i +40 i-50i^2 }{(-8)^2-(-10i)^2} = \frac{40-50i +40 i+50}{64 + 100} = \frac{90-10i }{164} = \frac{45}{82} + \frac{-5}{82}i \)
11. \((2+2i)+(9+4i)= 2+2i +9+4i =\color{red}{2+9}\color{blue}{+2i +4i}=\color{red}{11}\color{blue}{+6i}\)
12. \(\frac{7+9i}{-4+5i}= \frac{7+9i}{-4+5i} \cdot \frac{-4-5i}{-4-5i} = \frac{-28-35i -36 i-45i^2 }{(-4)^2-(5i)^2} = \frac{-28-35i -36 i+45}{16 + 25} = \frac{17-71i }{41} = \frac{17}{41} + \frac{-71}{41}i \)