Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((7-9i)+(2-2i)= 7-9i +2-2i =\color{red}{7+2}\color{blue}{-9i -2i}=\color{red}{9}\color{blue}{-11i}\)
2. \(\frac{7-10i}{-10-2i}= \frac{7-10i}{-10-2i} \cdot \frac{-10+2i}{-10+2i} = \frac{-70+14i +100 i-20i^2 }{(-10)^2-(-2i)^2} = \frac{-70+14i +100 i+20}{100 + 4} = \frac{-50+114i }{104} = \frac{-25}{52} - \frac{-57}{52}i \)
3. \((-10+5i)-(-5-2i)= -10+5i +5+2i =\color{red}{-10+5}\color{blue}{+5i +2i}=\color{red}{-5}\color{blue}{+7i}\)
4. \((-4+6i)\cdot (-6i)= +24 i-36i^2 = \color{red}{36}\color{blue}{+24i}\)
5. \((-10-3i)\cdot (-8i)= +80 i+24i^2 = \color{red}{-24}\color{blue}{+80i}\)
6. \((8+2i)-(-1+8i)= 8+2i +1-8i =\color{red}{8+1}\color{blue}{+2i -8i}=\color{red}{9}\color{blue}{-6i}\)
7. \((3-6i)+(-9-4i)= 3-6i -9-4i =\color{red}{3-9}\color{blue}{-6i -4i}=\color{red}{-6}\color{blue}{-10i}\)
8. \((9+9i)-(1-3i)= 9+9i -1+3i =\color{red}{9-1}\color{blue}{+9i +3i}=\color{red}{8}\color{blue}{+12i}\)
9. \((7+4i)-(7+10i)= 7+4i -7-10i =\color{red}{7-7}\color{blue}{+4i -10i}=\color{blue}{-6i}\)
10. \(\frac{4-6i}{6-9i}= \frac{4-6i}{6-9i} \cdot \frac{6+9i}{6+9i} = \frac{24+36i -36 i-54i^2 }{(6)^2-(-9i)^2} = \frac{24+36i -36 i+54}{36 + 81} = \frac{78+0i }{117} = \frac{2}{3} + 0i\)
11. \(\frac{10+9i}{-5-i}= \frac{10+9i}{-5-i} \cdot \frac{-5+i}{-5+i} = \frac{-50+10i -45 i+9i^2 }{(-5)^2-(-1i)^2} = \frac{-50+10i -45 i-9}{25 + 1} = \frac{-59-35i }{26} = \frac{-59}{26} + \frac{-35}{26}i \)
12. \((1+4i)-(-4-10i)= 1+4i +4+10i =\color{red}{1+4}\color{blue}{+4i +10i}=\color{red}{5}\color{blue}{+14i}\)