Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((3-6i) \cdot (-1+i)= -3+3i +6 i-6i^2 = -3+3i +6 i+6= \color{red}{-3+6}\color{blue}{+3i +6i}=\color{red}{3}\color{blue}{+9i}\)
2. \((9+8i)-(-6+4i)= 9+8i +6-4i =\color{red}{9+6}\color{blue}{+8i -4i}=\color{red}{15}\color{blue}{+4i}\)
3. \((-7+5i) \cdot (4-i)= -28+7i +20 i-5i^2 = -28+7i +20 i+5= \color{red}{-28+5}\color{blue}{+7i +20i}=\color{red}{-23}\color{blue}{+27i}\)
4. \(\frac{4-i}{10+10i}= \frac{4-i}{10+10i} \cdot \frac{10-10i}{10-10i} = \frac{40-40i -10 i+10i^2 }{(10)^2-(10i)^2} = \frac{40-40i -10 i-10}{100 + 100} = \frac{30-50i }{200} = \frac{3}{20} + \frac{-1}{4}i \)
5. \((1-6i)-(-7-i)= 1-6i +7+i =\color{red}{1+7}\color{blue}{-6i +i}=\color{red}{8}\color{blue}{-5i}\)
6. \((-9i) \cdot (-3+7i)= +27 i-63i^2 = \color{red}{63}\color{blue}{+27i}\)
7. \((-9i) \cdot (9+2i)= -81 i-18i^2 = \color{red}{18}\color{blue}{-81i}\)
8. \((8-4i)-(-1+10i)= 8-4i +1-10i =\color{red}{8+1}\color{blue}{-4i -10i}=\color{red}{9}\color{blue}{-14i}\)
9. \((-3-5i) \cdot (8+4i)= -24-12i -40 i-20i^2 = -24-12i -40 i+20= \color{red}{-24+20}\color{blue}{-12i -40i}=\color{red}{-4}\color{blue}{-52i}\)
10. \((-3+6i) \cdot (5-10i)= -15+30i +30 i-60i^2 = -15+30i +30 i+60= \color{red}{-15+60}\color{blue}{+30i +30i}=\color{red}{45}\color{blue}{+60i}\)
11. \((-8+6i)+(-2-3i)= -8+6i -2-3i =\color{red}{-8-2}\color{blue}{+6i -3i}=\color{red}{-10}\color{blue}{+3i}\)
12. \(\frac{-2+9i}{-6-10i}= \frac{-2+9i}{-6-10i} \cdot \frac{-6+10i}{-6+10i} = \frac{12-20i -54 i+90i^2 }{(-6)^2-(-10i)^2} = \frac{12-20i -54 i-90}{36 + 100} = \frac{-78-74i }{136} = \frac{-39}{68} + \frac{-37}{68}i \)