Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \((9+9i) \cdot (-8-10i)= -72-90i -72 i-90i^2 = -72-90i -72 i+90= \color{red}{-72+90}\color{blue}{-90i -72i}=\color{red}{18}\color{blue}{-162i}\)
2. \(\frac{-8+3i}{8-5i}= \frac{-8+3i}{8-5i} \cdot \frac{8+5i}{8+5i} = \frac{-64-40i +24 i+15i^2 }{(8)^2-(-5i)^2} = \frac{-64-40i +24 i-15}{64 + 25} = \frac{-79-16i }{89} = \frac{-79}{89} + \frac{-16}{89}i \)
3. \(\frac{-1+3i}{-9-10i}= \frac{-1+3i}{-9-10i} \cdot \frac{-9+10i}{-9+10i} = \frac{9-10i -27 i+30i^2 }{(-9)^2-(-10i)^2} = \frac{9-10i -27 i-30}{81 + 100} = \frac{-21-37i }{181} = \frac{-21}{181} + \frac{-37}{181}i \)
4. \((-4-i)-(-7-8i)= -4-i +7+8i =\color{red}{-4+7}\color{blue}{-i +8i}=\color{red}{3}\color{blue}{+7i}\)
5. \((-3+9i) \cdot (3-8i)= -9+24i +27 i-72i^2 = -9+24i +27 i+72= \color{red}{-9+72}\color{blue}{+24i +27i}=\color{red}{63}\color{blue}{+51i}\)
6. \((+2i) \cdot (-9+7i)= -18 i+14i^2 = \color{red}{-14}\color{blue}{-18i}\)
7. \((-3-6i) \cdot (6+8i)= -18-24i -36 i-48i^2 = -18-24i -36 i+48= \color{red}{-18+48}\color{blue}{-24i -36i}=\color{red}{30}\color{blue}{-60i}\)
8. \((-2+4i) \cdot (-7+5i)= 14-10i -28 i+20i^2 = 14-10i -28 i-20= \color{red}{14-20}\color{blue}{-10i -28i}=\color{red}{-6}\color{blue}{-38i}\)
9. \((-7+6i)+(5-4i)= -7+6i +5-4i =\color{red}{-7+5}\color{blue}{+6i -4i}=\color{red}{-2}\color{blue}{+2i}\)
10. \((-4+4i)\cdot (-5i)= +20 i-20i^2 = \color{red}{20}\color{blue}{+20i}\)
11. \(\frac{-3+10i}{6-10i}= \frac{-3+10i}{6-10i} \cdot \frac{6+10i}{6+10i} = \frac{-18-30i +60 i+100i^2 }{(6)^2-(-10i)^2} = \frac{-18-30i +60 i-100}{36 + 100} = \frac{-118+30i }{136} = \frac{-59}{68} - \frac{-15}{68}i \)
12. \(\frac{6-5i}{5+6i}= \frac{6-5i}{5+6i} \cdot \frac{5-6i}{5-6i} = \frac{30-36i -25 i+30i^2 }{(5)^2-(6i)^2} = \frac{30-36i -25 i-30}{25 + 36} = \frac{0-61i }{61} = 0+ 1i\)