Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((1+9i)+(5+5i)= 1+9i +5+5i =\color{red}{1+5}\color{blue}{+9i +5i}=\color{red}{6}\color{blue}{+14i}\)
2. \((7-3i)-(10-4i)= 7-3i -10+4i =\color{red}{7-10}\color{blue}{-3i +4i}=\color{red}{-3}\color{blue}{+i}\)
3. \((5-9i)-(-2+10i)= 5-9i +2-10i =\color{red}{5+2}\color{blue}{-9i -10i}=\color{red}{7}\color{blue}{-19i}\)
4. \(\frac{-8+i}{6-2i}= \frac{-8+i}{6-2i} \cdot \frac{6+2i}{6+2i} = \frac{-48-16i +6 i+2i^2 }{(6)^2-(-2i)^2} = \frac{-48-16i +6 i-2}{36 + 4} = \frac{-50-10i }{40} = \frac{-5}{4} + \frac{-1}{4}i \)
5. \((+i) \cdot (-7+8i)= -7 i+8i^2 = \color{red}{-8}\color{blue}{-7i}\)
6. \((+10i) \cdot (8+6i)= +80 i+60i^2 = \color{red}{-60}\color{blue}{+80i}\)
7. \((8+6i)+(-10+2i)= 8+6i -10+2i =\color{red}{8-10}\color{blue}{+6i +2i}=\color{red}{-2}\color{blue}{+8i}\)
8. \((-1+9i) \cdot (6+8i)= -6-8i +54 i+72i^2 = -6-8i +54 i-72= \color{red}{-6-72}\color{blue}{-8i +54i}=\color{red}{-78}\color{blue}{+46i}\)
9. \((-9+5i)\cdot (-2i)= +18 i-10i^2 = \color{red}{10}\color{blue}{+18i}\)
10. \((8-2i)+(-6+7i)= 8-2i -6+7i =\color{red}{8-6}\color{blue}{-2i +7i}=\color{red}{2}\color{blue}{+5i}\)
11. \((-6+6i)-(-9-6i)= -6+6i +9+6i =\color{red}{-6+9}\color{blue}{+6i +6i}=\color{red}{3}\color{blue}{+12i}\)
12. \((9+10i)\cdot (-3i)= -27 i-30i^2 = \color{red}{30}\color{blue}{-27i}\)