Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-5-9i) \cdot (7+7i)= -35-35i -63 i-63i^2 = -35-35i -63 i+63= \color{red}{-35+63}\color{blue}{-35i -63i}=\color{red}{28}\color{blue}{-98i}\)
2. \((-4-8i)-(1+10i)= -4-8i -1-10i =\color{red}{-4-1}\color{blue}{-8i -10i}=\color{red}{-5}\color{blue}{-18i}\)
3. \((-7+i)+(7+i)= -7+i +7+i =\color{red}{-7+7}\color{blue}{+i +i}=\color{blue}{2i}\)
4. \((-5-i)-(-8-2i)= -5-i +8+2i =\color{red}{-5+8}\color{blue}{-i +2i}=\color{red}{3}\color{blue}{+i}\)
5. \((-6-i)+(-3+9i)= -6-i -3+9i =\color{red}{-6-3}\color{blue}{-i +9i}=\color{red}{-9}\color{blue}{+8i}\)
6. \((-7i) \cdot (-2-8i)= +14 i+56i^2 = \color{red}{-56}\color{blue}{+14i}\)
7. \((10-7i) \cdot (4+5i)= 40+50i -28 i-35i^2 = 40+50i -28 i+35= \color{red}{40+35}\color{blue}{+50i -28i}=\color{red}{75}\color{blue}{+22i}\)
8. \(\frac{5-i}{6+7i}= \frac{5-i}{6+7i} \cdot \frac{6-7i}{6-7i} = \frac{30-35i -6 i+7i^2 }{(6)^2-(7i)^2} = \frac{30-35i -6 i-7}{36 + 49} = \frac{23-41i }{85} = \frac{23}{85} + \frac{-41}{85}i \)
9. \((-1-4i) \cdot (-2+2i)= 2-2i +8 i-8i^2 = 2-2i +8 i+8= \color{red}{2+8}\color{blue}{-2i +8i}=\color{red}{10}\color{blue}{+6i}\)
10. \((-5-10i)+(-4-2i)= -5-10i -4-2i =\color{red}{-5-4}\color{blue}{-10i -2i}=\color{red}{-9}\color{blue}{-12i}\)
11. \((-6+3i)-(3+7i)= -6+3i -3-7i =\color{red}{-6-3}\color{blue}{+3i -7i}=\color{red}{-9}\color{blue}{-4i}\)
12. \((1+9i)-(9-3i)= 1+9i -9+3i =\color{red}{1-9}\color{blue}{+9i +3i}=\color{red}{-8}\color{blue}{+12i}\)