Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{4+2i}{9-8i}= \frac{4+2i}{9-8i} \cdot \frac{9+8i}{9+8i} = \frac{36+32i +18 i+16i^2 }{(9)^2-(-8i)^2} = \frac{36+32i +18 i-16}{81 + 64} = \frac{20+50i }{145} = \frac{4}{29} - \frac{-10}{29}i \)
2. \((-9-9i)+(-7+i)= -9-9i -7+i =\color{red}{-9-7}\color{blue}{-9i +i}=\color{red}{-16}\color{blue}{-8i}\)
3. \((3+3i)+(-8+6i)= 3+3i -8+6i =\color{red}{3-8}\color{blue}{+3i +6i}=\color{red}{-5}\color{blue}{+9i}\)
4. \((4-4i)+(8+10i)= 4-4i +8+10i =\color{red}{4+8}\color{blue}{-4i +10i}=\color{red}{12}\color{blue}{+6i}\)
5. \((4-6i) \cdot (9-5i)= 36-20i -54 i+30i^2 = 36-20i -54 i-30= \color{red}{36-30}\color{blue}{-20i -54i}=\color{red}{6}\color{blue}{-74i}\)
6. \(\frac{-3-8i}{-1-6i}= \frac{-3-8i}{-1-6i} \cdot \frac{-1+6i}{-1+6i} = \frac{3-18i +8 i-48i^2 }{(-1)^2-(-6i)^2} = \frac{3-18i +8 i+48}{1 + 36} = \frac{51-10i }{37} = \frac{51}{37} + \frac{-10}{37}i \)
7. \((-7-10i) \cdot (1-4i)= -7+28i -10 i+40i^2 = -7+28i -10 i-40= \color{red}{-7-40}\color{blue}{+28i -10i}=\color{red}{-47}\color{blue}{+18i}\)
8. \((-3+3i)-(10-7i)= -3+3i -10+7i =\color{red}{-3-10}\color{blue}{+3i +7i}=\color{red}{-13}\color{blue}{+10i}\)
9. \((-3+i)\cdot (+5i)= -15 i+5i^2 = \color{red}{-5}\color{blue}{-15i}\)
10. \((-3-i)+(-6-5i)= -3-i -6-5i =\color{red}{-3-6}\color{blue}{-i -5i}=\color{red}{-9}\color{blue}{-6i}\)
11. \((3-4i)-(-10-9i)= 3-4i +10+9i =\color{red}{3+10}\color{blue}{-4i +9i}=\color{red}{13}\color{blue}{+5i}\)
12. \((-9-8i)+(-3+9i)= -9-8i -3+9i =\color{red}{-9-3}\color{blue}{-8i +9i}=\color{red}{-12}\color{blue}{+i}\)