Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((5-3i)+(-1-8i)= 5-3i -1-8i =\color{red}{5-1}\color{blue}{-3i -8i}=\color{red}{4}\color{blue}{-11i}\)
2. \((-7-9i) \cdot (2+4i)= -14-28i -18 i-36i^2 = -14-28i -18 i+36= \color{red}{-14+36}\color{blue}{-28i -18i}=\color{red}{22}\color{blue}{-46i}\)
3. \((9+3i) \cdot (-5-10i)= -45-90i -15 i-30i^2 = -45-90i -15 i+30= \color{red}{-45+30}\color{blue}{-90i -15i}=\color{red}{-15}\color{blue}{-105i}\)
4. \((7+7i) \cdot (-3+i)= -21+7i -21 i+7i^2 = -21+7i -21 i-7= \color{red}{-21-7}\color{blue}{+7i -21i}=\color{red}{-28}\color{blue}{-14i}\)
5. \(\frac{-4+2i}{10-i}= \frac{-4+2i}{10-i} \cdot \frac{10+i}{10+i} = \frac{-40-4i +20 i+2i^2 }{(10)^2-(-1i)^2} = \frac{-40-4i +20 i-2}{100 + 1} = \frac{-42+16i }{101} = \frac{-42}{101} - \frac{-16}{101}i \)
6. \((-7-8i)+(-2+2i)= -7-8i -2+2i =\color{red}{-7-2}\color{blue}{-8i +2i}=\color{red}{-9}\color{blue}{-6i}\)
7. \((7-6i) \cdot (5-9i)= 35-63i -30 i+54i^2 = 35-63i -30 i-54= \color{red}{35-54}\color{blue}{-63i -30i}=\color{red}{-19}\color{blue}{-93i}\)
8. \((-7+5i)+(2+5i)= -7+5i +2+5i =\color{red}{-7+2}\color{blue}{+5i +5i}=\color{red}{-5}\color{blue}{+10i}\)
9. \(\frac{7+4i}{3-7i}= \frac{7+4i}{3-7i} \cdot \frac{3+7i}{3+7i} = \frac{21+49i +12 i+28i^2 }{(3)^2-(-7i)^2} = \frac{21+49i +12 i-28}{9 + 49} = \frac{-7+61i }{58} = \frac{-7}{58} - \frac{-61}{58}i \)
10. \((+9i) \cdot (-1-7i)= -9 i-63i^2 = \color{red}{63}\color{blue}{-9i}\)
11. \(\frac{7+2i}{9+6i}= \frac{7+2i}{9+6i} \cdot \frac{9-6i}{9-6i} = \frac{63-42i +18 i-12i^2 }{(9)^2-(6i)^2} = \frac{63-42i +18 i+12}{81 + 36} = \frac{75-24i }{117} = \frac{25}{39} + \frac{-8}{39}i \)
12. \((-8-8i)+(-1-6i)= -8-8i -1-6i =\color{red}{-8-1}\color{blue}{-8i -6i}=\color{red}{-9}\color{blue}{-14i}\)