Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((+3i) \cdot (9-3i)= +27 i-9i^2 = \color{red}{9}\color{blue}{+27i}\)
2. \((-6+3i)+(3+8i)= -6+3i +3+8i =\color{red}{-6+3}\color{blue}{+3i +8i}=\color{red}{-3}\color{blue}{+11i}\)
3. \(\frac{-7-7i}{-6+i}= \frac{-7-7i}{-6+i} \cdot \frac{-6-i}{-6-i} = \frac{42+7i +42 i+7i^2 }{(-6)^2-(1i)^2} = \frac{42+7i +42 i-7}{36 + 1} = \frac{35+49i }{37} = \frac{35}{37} - \frac{-49}{37}i \)
4. \(\frac{-4+2i}{-10+6i}= \frac{-4+2i}{-10+6i} \cdot \frac{-10-6i}{-10-6i} = \frac{40+24i -20 i-12i^2 }{(-10)^2-(6i)^2} = \frac{40+24i -20 i+12}{100 + 36} = \frac{52+4i }{136} = \frac{13}{34} - \frac{-1}{34}i \)
5. \((9+8i)+(3-5i)= 9+8i +3-5i =\color{red}{9+3}\color{blue}{+8i -5i}=\color{red}{12}\color{blue}{+3i}\)
6. \((2+i)+(-10+i)= 2+i -10+i =\color{red}{2-10}\color{blue}{+i +i}=\color{red}{-8}\color{blue}{+2i}\)
7. \(\frac{2-6i}{7+i}= \frac{2-6i}{7+i} \cdot \frac{7-i}{7-i} = \frac{14-2i -42 i+6i^2 }{(7)^2-(1i)^2} = \frac{14-2i -42 i-6}{49 + 1} = \frac{8-44i }{50} = \frac{4}{25} + \frac{-22}{25}i \)
8. \(\frac{-6+3i}{-1+2i}= \frac{-6+3i}{-1+2i} \cdot \frac{-1-2i}{-1-2i} = \frac{6+12i -3 i-6i^2 }{(-1)^2-(2i)^2} = \frac{6+12i -3 i+6}{1 + 4} = \frac{12+9i }{5} = \frac{12}{5} - \frac{-9}{5}i \)
9. \((7+9i)\cdot (-3i)= -21 i-27i^2 = \color{red}{27}\color{blue}{-21i}\)
10. \(\frac{-4-8i}{8-10i}= \frac{-4-8i}{8-10i} \cdot \frac{8+10i}{8+10i} = \frac{-32-40i -64 i-80i^2 }{(8)^2-(-10i)^2} = \frac{-32-40i -64 i+80}{64 + 100} = \frac{48-104i }{164} = \frac{12}{41} + \frac{-26}{41}i \)
11. \((-1+10i) \cdot (5-3i)= -5+3i +50 i-30i^2 = -5+3i +50 i+30= \color{red}{-5+30}\color{blue}{+3i +50i}=\color{red}{25}\color{blue}{+53i}\)
12. \((8+3i) \cdot (3+3i)= 24+24i +9 i+9i^2 = 24+24i +9 i-9= \color{red}{24-9}\color{blue}{+24i +9i}=\color{red}{15}\color{blue}{+33i}\)