Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-10-i}{-10+4i}= \frac{-10-i}{-10+4i} \cdot \frac{-10-4i}{-10-4i} = \frac{100+40i +10 i+4i^2 }{(-10)^2-(4i)^2} = \frac{100+40i +10 i-4}{100 + 16} = \frac{96+50i }{116} = \frac{24}{29} - \frac{-25}{58}i \)
2. \((-1+i)+(4-2i)= -1+i +4-2i =\color{red}{-1+4}\color{blue}{+i -2i}=\color{red}{3}\color{blue}{-i}\)
3. \((1+9i)+(-8+8i)= 1+9i -8+8i =\color{red}{1-8}\color{blue}{+9i +8i}=\color{red}{-7}\color{blue}{+17i}\)
4. \((-7+6i)+(9-4i)= -7+6i +9-4i =\color{red}{-7+9}\color{blue}{+6i -4i}=\color{red}{2}\color{blue}{+2i}\)
5. \((6+6i)-(1+4i)= 6+6i -1-4i =\color{red}{6-1}\color{blue}{+6i -4i}=\color{red}{5}\color{blue}{+2i}\)
6. \((4+6i)+(-2+3i)= 4+6i -2+3i =\color{red}{4-2}\color{blue}{+6i +3i}=\color{red}{2}\color{blue}{+9i}\)
7. \((9+7i) \cdot (-7+10i)= -63+90i -49 i+70i^2 = -63+90i -49 i-70= \color{red}{-63-70}\color{blue}{+90i -49i}=\color{red}{-133}\color{blue}{+41i}\)
8. \((-4-7i)-(-6+3i)= -4-7i +6-3i =\color{red}{-4+6}\color{blue}{-7i -3i}=\color{red}{2}\color{blue}{-10i}\)
9. \((2+7i)+(7-2i)= 2+7i +7-2i =\color{red}{2+7}\color{blue}{+7i -2i}=\color{red}{9}\color{blue}{+5i}\)
10. \((+2i) \cdot (9-5i)= +18 i-10i^2 = \color{red}{10}\color{blue}{+18i}\)
11. \((10-5i) \cdot (7-9i)= 70-90i -35 i+45i^2 = 70-90i -35 i-45= \color{red}{70-45}\color{blue}{-90i -35i}=\color{red}{25}\color{blue}{-125i}\)
12. \((10-10i) \cdot (-1+2i)= -10+20i +10 i-20i^2 = -10+20i +10 i+20= \color{red}{-10+20}\color{blue}{+20i +10i}=\color{red}{10}\color{blue}{+30i}\)