Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7-8i)-(9-2i)= 7-8i -9+2i =\color{red}{7-9}\color{blue}{-8i +2i}=\color{red}{-2}\color{blue}{-6i}\)
2. \((5-4i) \cdot (-3+4i)= -15+20i +12 i-16i^2 = -15+20i +12 i+16= \color{red}{-15+16}\color{blue}{+20i +12i}=\color{red}{1}\color{blue}{+32i}\)
3. \((-5+10i) \cdot (3+9i)= -15-45i +30 i+90i^2 = -15-45i +30 i-90= \color{red}{-15-90}\color{blue}{-45i +30i}=\color{red}{-105}\color{blue}{-15i}\)
4. \(\frac{3-10i}{7-6i}= \frac{3-10i}{7-6i} \cdot \frac{7+6i}{7+6i} = \frac{21+18i -70 i-60i^2 }{(7)^2-(-6i)^2} = \frac{21+18i -70 i+60}{49 + 36} = \frac{81-52i }{85} = \frac{81}{85} + \frac{-52}{85}i \)
5. \(\frac{-5-8i}{4+4i}= \frac{-5-8i}{4+4i} \cdot \frac{4-4i}{4-4i} = \frac{-20+20i -32 i+32i^2 }{(4)^2-(4i)^2} = \frac{-20+20i -32 i-32}{16 + 16} = \frac{-52-12i }{32} = \frac{-13}{8} + \frac{-3}{8}i \)
6. \(\frac{5+5i}{-4+7i}= \frac{5+5i}{-4+7i} \cdot \frac{-4-7i}{-4-7i} = \frac{-20-35i -20 i-35i^2 }{(-4)^2-(7i)^2} = \frac{-20-35i -20 i+35}{16 + 49} = \frac{15-55i }{65} = \frac{3}{13} + \frac{-11}{13}i \)
7. \((-3+5i)-(-10-10i)= -3+5i +10+10i =\color{red}{-3+10}\color{blue}{+5i +10i}=\color{red}{7}\color{blue}{+15i}\)
8. \((-3-6i)-(7+7i)= -3-6i -7-7i =\color{red}{-3-7}\color{blue}{-6i -7i}=\color{red}{-10}\color{blue}{-13i}\)
9. \(\frac{2-4i}{-5+5i}= \frac{2-4i}{-5+5i} \cdot \frac{-5-5i}{-5-5i} = \frac{-10-10i +20 i+20i^2 }{(-5)^2-(5i)^2} = \frac{-10-10i +20 i-20}{25 + 25} = \frac{-30+10i }{50} = \frac{-3}{5} - \frac{-1}{5}i \)
10. \((6+2i) \cdot (-1+2i)= -6+12i -2 i+4i^2 = -6+12i -2 i-4= \color{red}{-6-4}\color{blue}{+12i -2i}=\color{red}{-10}\color{blue}{+10i}\)
11. \((-5+2i) \cdot (-10-5i)= 50+25i -20 i-10i^2 = 50+25i -20 i+10= \color{red}{50+10}\color{blue}{+25i -20i}=\color{red}{60}\color{blue}{+5i}\)
12. \((-3i) \cdot (2-10i)= -6 i+30i^2 = \color{red}{-30}\color{blue}{-6i}\)