Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{-10+5i}{7-6i}= \frac{-10+5i}{7-6i} \cdot \frac{7+6i}{7+6i} = \frac{-70-60i +35 i+30i^2 }{(7)^2-(-6i)^2} = \frac{-70-60i +35 i-30}{49 + 36} = \frac{-100-25i }{85} = \frac{-20}{17} + \frac{-5}{17}i \)
2. \((8-6i)+(6+6i)= 8-6i +6+6i =\color{red}{8+6}\color{blue}{-6i +6i}=\color{red}{14}\)
3. \((-10-4i)+(2-2i)= -10-4i +2-2i =\color{red}{-10+2}\color{blue}{-4i -2i}=\color{red}{-8}\color{blue}{-6i}\)
4. \((-10+3i)-(9+10i)= -10+3i -9-10i =\color{red}{-10-9}\color{blue}{+3i -10i}=\color{red}{-19}\color{blue}{-7i}\)
5. \((4-8i)-(8+6i)= 4-8i -8-6i =\color{red}{4-8}\color{blue}{-8i -6i}=\color{red}{-4}\color{blue}{-14i}\)
6. \((6+3i)+(-2-8i)= 6+3i -2-8i =\color{red}{6-2}\color{blue}{+3i -8i}=\color{red}{4}\color{blue}{-5i}\)
7. \((10+10i) \cdot (1+8i)= 10+80i +10 i+80i^2 = 10+80i +10 i-80= \color{red}{10-80}\color{blue}{+80i +10i}=\color{red}{-70}\color{blue}{+90i}\)
8. \((10+10i)-(-9-4i)= 10+10i +9+4i =\color{red}{10+9}\color{blue}{+10i +4i}=\color{red}{19}\color{blue}{+14i}\)
9. \((9+3i)+(-1+i)= 9+3i -1+i =\color{red}{9-1}\color{blue}{+3i +i}=\color{red}{8}\color{blue}{+4i}\)
10. \((-4-8i) \cdot (5-4i)= -20+16i -40 i+32i^2 = -20+16i -40 i-32= \color{red}{-20-32}\color{blue}{+16i -40i}=\color{red}{-52}\color{blue}{-24i}\)
11. \((-1-10i)-(-3-3i)= -1-10i +3+3i =\color{red}{-1+3}\color{blue}{-10i +3i}=\color{red}{2}\color{blue}{-7i}\)
12. \(\frac{-7+8i}{4-2i}= \frac{-7+8i}{4-2i} \cdot \frac{4+2i}{4+2i} = \frac{-28-14i +32 i+16i^2 }{(4)^2-(-2i)^2} = \frac{-28-14i +32 i-16}{16 + 4} = \frac{-44+18i }{20} = \frac{-11}{5} - \frac{-9}{10}i \)