Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((10-3i) \cdot (4+7i)= 40+70i -12 i-21i^2 = 40+70i -12 i+21= \color{red}{40+21}\color{blue}{+70i -12i}=\color{red}{61}\color{blue}{+58i}\)
2. \(\frac{2+10i}{7+2i}= \frac{2+10i}{7+2i} \cdot \frac{7-2i}{7-2i} = \frac{14-4i +70 i-20i^2 }{(7)^2-(2i)^2} = \frac{14-4i +70 i+20}{49 + 4} = \frac{34+66i }{53} = \frac{34}{53} - \frac{-66}{53}i \)
3. \((-3+3i)\cdot (+5i)= -15 i+15i^2 = \color{red}{-15}\color{blue}{-15i}\)
4. \((+10i) \cdot (-4+3i)= -40 i+30i^2 = \color{red}{-30}\color{blue}{-40i}\)
5. \((8-10i)-(9-3i)= 8-10i -9+3i =\color{red}{8-9}\color{blue}{-10i +3i}=\color{red}{-1}\color{blue}{-7i}\)
6. \((-5+10i)+(5-4i)= -5+10i +5-4i =\color{red}{-5+5}\color{blue}{+10i -4i}=\color{blue}{6i}\)
7. \((-9-4i)+(-8+7i)= -9-4i -8+7i =\color{red}{-9-8}\color{blue}{-4i +7i}=\color{red}{-17}\color{blue}{+3i}\)
8. \((-6-6i)+(-6+6i)= -6-6i -6+6i =\color{red}{-6-6}\color{blue}{-6i +6i}=\color{red}{-12}\)
9. \((-5-8i) \cdot (7+7i)= -35-35i -56 i-56i^2 = -35-35i -56 i+56= \color{red}{-35+56}\color{blue}{-35i -56i}=\color{red}{21}\color{blue}{-91i}\)
10. \((7+7i)-(2+3i)= 7+7i -2-3i =\color{red}{7-2}\color{blue}{+7i -3i}=\color{red}{5}\color{blue}{+4i}\)
11. \((5+9i)\cdot (-i)= -5 i-9i^2 = \color{red}{9}\color{blue}{-5i}\)
12. \((7+6i) \cdot (-7+5i)= -49+35i -42 i+30i^2 = -49+35i -42 i-30= \color{red}{-49-30}\color{blue}{+35i -42i}=\color{red}{-79}\color{blue}{-7i}\)