Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((-10+2i)-(2-i)= -10+2i -2+i =\color{red}{-10-2}\color{blue}{+2i +i}=\color{red}{-12}\color{blue}{+3i}\)
2. \((7+5i) \cdot (-10-2i)= -70-14i -50 i-10i^2 = -70-14i -50 i+10= \color{red}{-70+10}\color{blue}{-14i -50i}=\color{red}{-60}\color{blue}{-64i}\)
3. \((1+2i)\cdot (-8i)= -8 i-16i^2 = \color{red}{16}\color{blue}{-8i}\)
4. \((+i) \cdot (-1+7i)= -1 i+7i^2 = \color{red}{-7}\color{blue}{-i}\)
5. \((5+3i)+(9-8i)= 5+3i +9-8i =\color{red}{5+9}\color{blue}{+3i -8i}=\color{red}{14}\color{blue}{-5i}\)
6. \((-5+4i) \cdot (3-3i)= -15+15i +12 i-12i^2 = -15+15i +12 i+12= \color{red}{-15+12}\color{blue}{+15i +12i}=\color{red}{-3}\color{blue}{+27i}\)
7. \((+8i) \cdot (-1+2i)= -8 i+16i^2 = \color{red}{-16}\color{blue}{-8i}\)
8. \((+9i) \cdot (-4+4i)= -36 i+36i^2 = \color{red}{-36}\color{blue}{-36i}\)
9. \((5+2i)+(1+4i)= 5+2i +1+4i =\color{red}{5+1}\color{blue}{+2i +4i}=\color{red}{6}\color{blue}{+6i}\)
10. \(\frac{3-i}{8+10i}= \frac{3-i}{8+10i} \cdot \frac{8-10i}{8-10i} = \frac{24-30i -8 i+10i^2 }{(8)^2-(10i)^2} = \frac{24-30i -8 i-10}{64 + 100} = \frac{14-38i }{164} = \frac{7}{82} + \frac{-19}{82}i \)
11. \((7+6i) \cdot (5+9i)= 35+63i +30 i+54i^2 = 35+63i +30 i-54= \color{red}{35-54}\color{blue}{+63i +30i}=\color{red}{-19}\color{blue}{+93i}\)
12. \((-10+2i)-(-9-3i)= -10+2i +9+3i =\color{red}{-10+9}\color{blue}{+2i +3i}=\color{red}{-1}\color{blue}{+5i}\)