Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-1+5i)\cdot (+3i)= -3 i+15i^2 = \color{red}{-15}\color{blue}{-3i}\)
2. \(\frac{-9-7i}{2+8i}= \frac{-9-7i}{2+8i} \cdot \frac{2-8i}{2-8i} = \frac{-18+72i -14 i+56i^2 }{(2)^2-(8i)^2} = \frac{-18+72i -14 i-56}{4 + 64} = \frac{-74+58i }{68} = \frac{-37}{34} - \frac{-29}{34}i \)
3. \((-6+9i) \cdot (-6-3i)= 36+18i -54 i-27i^2 = 36+18i -54 i+27= \color{red}{36+27}\color{blue}{+18i -54i}=\color{red}{63}\color{blue}{-36i}\)
4. \((5-5i)+(-9+2i)= 5-5i -9+2i =\color{red}{5-9}\color{blue}{-5i +2i}=\color{red}{-4}\color{blue}{-3i}\)
5. \(\frac{8+2i}{10-5i}= \frac{8+2i}{10-5i} \cdot \frac{10+5i}{10+5i} = \frac{80+40i +20 i+10i^2 }{(10)^2-(-5i)^2} = \frac{80+40i +20 i-10}{100 + 25} = \frac{70+60i }{125} = \frac{14}{25} - \frac{-12}{25}i \)
6. \((1-9i)+(-3+6i)= 1-9i -3+6i =\color{red}{1-3}\color{blue}{-9i +6i}=\color{red}{-2}\color{blue}{-3i}\)
7. \((-7-i)+(-2-4i)= -7-i -2-4i =\color{red}{-7-2}\color{blue}{-i -4i}=\color{red}{-9}\color{blue}{-5i}\)
8. \((4-6i) \cdot (-7+8i)= -28+32i +42 i-48i^2 = -28+32i +42 i+48= \color{red}{-28+48}\color{blue}{+32i +42i}=\color{red}{20}\color{blue}{+74i}\)
9. \((3+10i) \cdot (-5+9i)= -15+27i -50 i+90i^2 = -15+27i -50 i-90= \color{red}{-15-90}\color{blue}{+27i -50i}=\color{red}{-105}\color{blue}{-23i}\)
10. \((1+10i)-(-9+3i)= 1+10i +9-3i =\color{red}{1+9}\color{blue}{+10i -3i}=\color{red}{10}\color{blue}{+7i}\)
11. \((7-6i)-(-10-8i)= 7-6i +10+8i =\color{red}{7+10}\color{blue}{-6i +8i}=\color{red}{17}\color{blue}{+2i}\)
12. \((-7-i)-(5-5i)= -7-i -5+5i =\color{red}{-7-5}\color{blue}{-i +5i}=\color{red}{-12}\color{blue}{+4i}\)