Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-2+5i)+(-9+10i)= -2+5i -9+10i =\color{red}{-2-9}\color{blue}{+5i +10i}=\color{red}{-11}\color{blue}{+15i}\)
2. \((7-10i) \cdot (2+4i)= 14+28i -20 i-40i^2 = 14+28i -20 i+40= \color{red}{14+40}\color{blue}{+28i -20i}=\color{red}{54}\color{blue}{+8i}\)
3. \((7-i)+(3+4i)= 7-i +3+4i =\color{red}{7+3}\color{blue}{-i +4i}=\color{red}{10}\color{blue}{+3i}\)
4. \((-4+2i) \cdot (1+8i)= -4-32i +2 i+16i^2 = -4-32i +2 i-16= \color{red}{-4-16}\color{blue}{-32i +2i}=\color{red}{-20}\color{blue}{-30i}\)
5. \((-5-10i)-(-8+3i)= -5-10i +8-3i =\color{red}{-5+8}\color{blue}{-10i -3i}=\color{red}{3}\color{blue}{-13i}\)
6. \((1+9i) \cdot (3+9i)= 3+9i +27 i+81i^2 = 3+9i +27 i-81= \color{red}{3-81}\color{blue}{+9i +27i}=\color{red}{-78}\color{blue}{+36i}\)
7. \((-4-7i)+(6+i)= -4-7i +6+i =\color{red}{-4+6}\color{blue}{-7i +i}=\color{red}{2}\color{blue}{-6i}\)
8. \((10-8i)-(-4-3i)= 10-8i +4+3i =\color{red}{10+4}\color{blue}{-8i +3i}=\color{red}{14}\color{blue}{-5i}\)
9. \((-1-i)\cdot (+7i)= -7 i-7i^2 = \color{red}{7}\color{blue}{-7i}\)
10. \((3+7i)+(-10+4i)= 3+7i -10+4i =\color{red}{3-10}\color{blue}{+7i +4i}=\color{red}{-7}\color{blue}{+11i}\)
11. \(\frac{8+2i}{-2-5i}= \frac{8+2i}{-2-5i} \cdot \frac{-2+5i}{-2+5i} = \frac{-16+40i -4 i+10i^2 }{(-2)^2-(-5i)^2} = \frac{-16+40i -4 i-10}{4 + 25} = \frac{-26+36i }{29} = \frac{-26}{29} - \frac{-36}{29}i \)
12. \(\frac{-2-9i}{9+4i}= \frac{-2-9i}{9+4i} \cdot \frac{9-4i}{9-4i} = \frac{-18+8i -81 i+36i^2 }{(9)^2-(4i)^2} = \frac{-18+8i -81 i-36}{81 + 16} = \frac{-54-73i }{97} = \frac{-54}{97} + \frac{-73}{97}i \)