Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((10+4i)-(7+8i)= 10+4i -7-8i =\color{red}{10-7}\color{blue}{+4i -8i}=\color{red}{3}\color{blue}{-4i}\)
2. \((7-10i)-(-5-8i)= 7-10i +5+8i =\color{red}{7+5}\color{blue}{-10i +8i}=\color{red}{12}\color{blue}{-2i}\)
3. \((8-5i)-(2+4i)= 8-5i -2-4i =\color{red}{8-2}\color{blue}{-5i -4i}=\color{red}{6}\color{blue}{-9i}\)
4. \((2+7i)+(-10+4i)= 2+7i -10+4i =\color{red}{2-10}\color{blue}{+7i +4i}=\color{red}{-8}\color{blue}{+11i}\)
5. \((-5-4i)-(7+9i)= -5-4i -7-9i =\color{red}{-5-7}\color{blue}{-4i -9i}=\color{red}{-12}\color{blue}{-13i}\)
6. \((+7i) \cdot (7+6i)= +49 i+42i^2 = \color{red}{-42}\color{blue}{+49i}\)
7. \((-8+2i) \cdot (3+8i)= -24-64i +6 i+16i^2 = -24-64i +6 i-16= \color{red}{-24-16}\color{blue}{-64i +6i}=\color{red}{-40}\color{blue}{-58i}\)
8. \((-8-i)\cdot (-7i)= +56 i+7i^2 = \color{red}{-7}\color{blue}{+56i}\)
9. \((-2+4i) \cdot (-1-6i)= 2+12i -4 i-24i^2 = 2+12i -4 i+24= \color{red}{2+24}\color{blue}{+12i -4i}=\color{red}{26}\color{blue}{+8i}\)
10. \((8+10i) \cdot (-2+10i)= -16+80i -20 i+100i^2 = -16+80i -20 i-100= \color{red}{-16-100}\color{blue}{+80i -20i}=\color{red}{-116}\color{blue}{+60i}\)
11. \(\frac{-3-3i}{-5-4i}= \frac{-3-3i}{-5-4i} \cdot \frac{-5+4i}{-5+4i} = \frac{15-12i +15 i-12i^2 }{(-5)^2-(-4i)^2} = \frac{15-12i +15 i+12}{25 + 16} = \frac{27+3i }{41} = \frac{27}{41} - \frac{-3}{41}i \)
12. \((3-3i)+(-7-i)= 3-3i -7-i =\color{red}{3-7}\color{blue}{-3i -i}=\color{red}{-4}\color{blue}{-4i}\)