Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-3+2i)+(2-2i)= -3+2i +2-2i =\color{red}{-3+2}\color{blue}{+2i -2i}=\color{red}{-1}\)
2. \((-1+10i)+(-9-3i)= -1+10i -9-3i =\color{red}{-1-9}\color{blue}{+10i -3i}=\color{red}{-10}\color{blue}{+7i}\)
3. \((2-9i) \cdot (10-10i)= 20-20i -90 i+90i^2 = 20-20i -90 i-90= \color{red}{20-90}\color{blue}{-20i -90i}=\color{red}{-70}\color{blue}{-110i}\)
4. \((-9+i)+(-1-3i)= -9+i -1-3i =\color{red}{-9-1}\color{blue}{+i -3i}=\color{red}{-10}\color{blue}{-2i}\)
5. \((4+8i)-(6+10i)= 4+8i -6-10i =\color{red}{4-6}\color{blue}{+8i -10i}=\color{red}{-2}\color{blue}{-2i}\)
6. \((7+5i)\cdot (+2i)= +14 i+10i^2 = \color{red}{-10}\color{blue}{+14i}\)
7. \((9-i)+(-10-10i)= 9-i -10-10i =\color{red}{9-10}\color{blue}{-i -10i}=\color{red}{-1}\color{blue}{-11i}\)
8. \((3-6i)-(-5+8i)= 3-6i +5-8i =\color{red}{3+5}\color{blue}{-6i -8i}=\color{red}{8}\color{blue}{-14i}\)
9. \(\frac{3+5i}{5+2i}= \frac{3+5i}{5+2i} \cdot \frac{5-2i}{5-2i} = \frac{15-6i +25 i-10i^2 }{(5)^2-(2i)^2} = \frac{15-6i +25 i+10}{25 + 4} = \frac{25+19i }{29} = \frac{25}{29} - \frac{-19}{29}i \)
10. \((3+3i)+(4-10i)= 3+3i +4-10i =\color{red}{3+4}\color{blue}{+3i -10i}=\color{red}{7}\color{blue}{-7i}\)
11. \((-5-7i)-(6+i)= -5-7i -6-i =\color{red}{-5-6}\color{blue}{-7i -i}=\color{red}{-11}\color{blue}{-8i}\)
12. \((9+9i)\cdot (-2i)= -18 i-18i^2 = \color{red}{18}\color{blue}{-18i}\)