Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-7-2i)-(-7+3i)= -7-2i +7-3i =\color{red}{-7+7}\color{blue}{-2i -3i}=\color{blue}{-5i}\)
2. \((-7+3i)\cdot (-2i)= +14 i-6i^2 = \color{red}{6}\color{blue}{+14i}\)
3. \(\frac{-4-7i}{6+4i}= \frac{-4-7i}{6+4i} \cdot \frac{6-4i}{6-4i} = \frac{-24+16i -42 i+28i^2 }{(6)^2-(4i)^2} = \frac{-24+16i -42 i-28}{36 + 16} = \frac{-52-26i }{52} = -1+ \frac{-1}{2}i \)
4. \((-3+2i)-(8+6i)= -3+2i -8-6i =\color{red}{-3-8}\color{blue}{+2i -6i}=\color{red}{-11}\color{blue}{-4i}\)
5. \(\frac{8-6i}{2-8i}= \frac{8-6i}{2-8i} \cdot \frac{2+8i}{2+8i} = \frac{16+64i -12 i-48i^2 }{(2)^2-(-8i)^2} = \frac{16+64i -12 i+48}{4 + 64} = \frac{64+52i }{68} = \frac{16}{17} - \frac{-13}{17}i \)
6. \((8-7i)-(1-6i)= 8-7i -1+6i =\color{red}{8-1}\color{blue}{-7i +6i}=\color{red}{7}\color{blue}{-i}\)
7. \(\frac{1-i}{9+5i}= \frac{1-i}{9+5i} \cdot \frac{9-5i}{9-5i} = \frac{9-5i -9 i+5i^2 }{(9)^2-(5i)^2} = \frac{9-5i -9 i-5}{81 + 25} = \frac{4-14i }{106} = \frac{2}{53} + \frac{-7}{53}i \)
8. \((-10+9i)+(-8+7i)= -10+9i -8+7i =\color{red}{-10-8}\color{blue}{+9i +7i}=\color{red}{-18}\color{blue}{+16i}\)
9. \(\frac{-2-3i}{6-4i}= \frac{-2-3i}{6-4i} \cdot \frac{6+4i}{6+4i} = \frac{-12-8i -18 i-12i^2 }{(6)^2-(-4i)^2} = \frac{-12-8i -18 i+12}{36 + 16} = \frac{0-26i }{52} = 0+ \frac{-1}{2}i \)
10. \((1-i)-(4+9i)= 1-i -4-9i =\color{red}{1-4}\color{blue}{-i -9i}=\color{red}{-3}\color{blue}{-10i}\)
11. \((-10+i)-(9+10i)= -10+i -9-10i =\color{red}{-10-9}\color{blue}{+i -10i}=\color{red}{-19}\color{blue}{-9i}\)
12. \((-6-5i)\cdot (-4i)= +24 i+20i^2 = \color{red}{-20}\color{blue}{+24i}\)