Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-9+9i)-(-6+i)= -9+9i +6-i =\color{red}{-9+6}\color{blue}{+9i -i}=\color{red}{-3}\color{blue}{+8i}\)
2. \((8-3i)+(-6-3i)= 8-3i -6-3i =\color{red}{8-6}\color{blue}{-3i -3i}=\color{red}{2}\color{blue}{-6i}\)
3. \((9-3i)+(5+i)= 9-3i +5+i =\color{red}{9+5}\color{blue}{-3i +i}=\color{red}{14}\color{blue}{-2i}\)
4. \(\frac{7-6i}{-2-4i}= \frac{7-6i}{-2-4i} \cdot \frac{-2+4i}{-2+4i} = \frac{-14+28i +12 i-24i^2 }{(-2)^2-(-4i)^2} = \frac{-14+28i +12 i+24}{4 + 16} = \frac{10+40i }{20} = \frac{1}{2} - -2i\)
5. \((3-8i)+(-3+6i)= 3-8i -3+6i =\color{red}{3-3}\color{blue}{-8i +6i}=\color{blue}{-2i}\)
6. \((-1+6i)+(-10-7i)= -1+6i -10-7i =\color{red}{-1-10}\color{blue}{+6i -7i}=\color{red}{-11}\color{blue}{-i}\)
7. \((2-3i)-(5+6i)= 2-3i -5-6i =\color{red}{2-5}\color{blue}{-3i -6i}=\color{red}{-3}\color{blue}{-9i}\)
8. \((7+5i) \cdot (1+4i)= 7+28i +5 i+20i^2 = 7+28i +5 i-20= \color{red}{7-20}\color{blue}{+28i +5i}=\color{red}{-13}\color{blue}{+33i}\)
9. \((7+2i)-(5-5i)= 7+2i -5+5i =\color{red}{7-5}\color{blue}{+2i +5i}=\color{red}{2}\color{blue}{+7i}\)
10. \(\frac{8-6i}{-3+4i}= \frac{8-6i}{-3+4i} \cdot \frac{-3-4i}{-3-4i} = \frac{-24-32i +18 i+24i^2 }{(-3)^2-(4i)^2} = \frac{-24-32i +18 i-24}{9 + 16} = \frac{-48-14i }{25} = \frac{-48}{25} + \frac{-14}{25}i \)
11. \((+8i) \cdot (2+2i)= +16 i+16i^2 = \color{red}{-16}\color{blue}{+16i}\)
12. \((1+3i)+(6+5i)= 1+3i +6+5i =\color{red}{1+6}\color{blue}{+3i +5i}=\color{red}{7}\color{blue}{+8i}\)