Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((3-2i)+(4-7i)= 3-2i +4-7i =\color{red}{3+4}\color{blue}{-2i -7i}=\color{red}{7}\color{blue}{-9i}\)
2. \((+3i) \cdot (-7+7i)= -21 i+21i^2 = \color{red}{-21}\color{blue}{-21i}\)
3. \((-5-5i)+(8+7i)= -5-5i +8+7i =\color{red}{-5+8}\color{blue}{-5i +7i}=\color{red}{3}\color{blue}{+2i}\)
4. \((6-3i) \cdot (6-4i)= 36-24i -18 i+12i^2 = 36-24i -18 i-12= \color{red}{36-12}\color{blue}{-24i -18i}=\color{red}{24}\color{blue}{-42i}\)
5. \((6-2i)+(-10-6i)= 6-2i -10-6i =\color{red}{6-10}\color{blue}{-2i -6i}=\color{red}{-4}\color{blue}{-8i}\)
6. \(\frac{-8-8i}{10-i}= \frac{-8-8i}{10-i} \cdot \frac{10+i}{10+i} = \frac{-80-8i -80 i-8i^2 }{(10)^2-(-1i)^2} = \frac{-80-8i -80 i+8}{100 + 1} = \frac{-72-88i }{101} = \frac{-72}{101} + \frac{-88}{101}i \)
7. \((1+7i) \cdot (1-8i)= 1-8i +7 i-56i^2 = 1-8i +7 i+56= \color{red}{1+56}\color{blue}{-8i +7i}=\color{red}{57}\color{blue}{-i}\)
8. \((2+9i)\cdot (-8i)= -16 i-72i^2 = \color{red}{72}\color{blue}{-16i}\)
9. \((-9+7i) \cdot (8+8i)= -72-72i +56 i+56i^2 = -72-72i +56 i-56= \color{red}{-72-56}\color{blue}{-72i +56i}=\color{red}{-128}\color{blue}{-16i}\)
10. \((-8+9i) \cdot (3+7i)= -24-56i +27 i+63i^2 = -24-56i +27 i-63= \color{red}{-24-63}\color{blue}{-56i +27i}=\color{red}{-87}\color{blue}{-29i}\)
11. \((10+5i) \cdot (-2+10i)= -20+100i -10 i+50i^2 = -20+100i -10 i-50= \color{red}{-20-50}\color{blue}{+100i -10i}=\color{red}{-70}\color{blue}{+90i}\)
12. \((-9-5i)\cdot (-4i)= +36 i+20i^2 = \color{red}{-20}\color{blue}{+36i}\)