Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{1+4i}{-3-8i}= \frac{1+4i}{-3-8i} \cdot \frac{-3+8i}{-3+8i} = \frac{-3+8i -12 i+32i^2 }{(-3)^2-(-8i)^2} = \frac{-3+8i -12 i-32}{9 + 64} = \frac{-35-4i }{73} = \frac{-35}{73} + \frac{-4}{73}i \)
2. \(\frac{-3+10i}{5+9i}= \frac{-3+10i}{5+9i} \cdot \frac{5-9i}{5-9i} = \frac{-15+27i +50 i-90i^2 }{(5)^2-(9i)^2} = \frac{-15+27i +50 i+90}{25 + 81} = \frac{75+77i }{106} = \frac{75}{106} - \frac{-77}{106}i \)
3. \((5-2i)-(-7+8i)= 5-2i +7-8i =\color{red}{5+7}\color{blue}{-2i -8i}=\color{red}{12}\color{blue}{-10i}\)
4. \(\frac{6+i}{-1-5i}= \frac{6+i}{-1-5i} \cdot \frac{-1+5i}{-1+5i} = \frac{-6+30i -1 i+5i^2 }{(-1)^2-(-5i)^2} = \frac{-6+30i -1 i-5}{1 + 25} = \frac{-11+29i }{26} = \frac{-11}{26} - \frac{-29}{26}i \)
5. \((2-6i)-(-6-5i)= 2-6i +6+5i =\color{red}{2+6}\color{blue}{-6i +5i}=\color{red}{8}\color{blue}{-i}\)
6. \((7+3i)\cdot (-10i)= -70 i-30i^2 = \color{red}{30}\color{blue}{-70i}\)
7. \((3+8i)-(-5-i)= 3+8i +5+i =\color{red}{3+5}\color{blue}{+8i +i}=\color{red}{8}\color{blue}{+9i}\)
8. \((4+i)\cdot (-10i)= -40 i-10i^2 = \color{red}{10}\color{blue}{-40i}\)
9. \((1-7i)-(9+8i)= 1-7i -9-8i =\color{red}{1-9}\color{blue}{-7i -8i}=\color{red}{-8}\color{blue}{-15i}\)
10. \(\frac{3+9i}{3+7i}= \frac{3+9i}{3+7i} \cdot \frac{3-7i}{3-7i} = \frac{9-21i +27 i-63i^2 }{(3)^2-(7i)^2} = \frac{9-21i +27 i+63}{9 + 49} = \frac{72+6i }{58} = \frac{36}{29} - \frac{-3}{29}i \)
11. \((+4i) \cdot (-4+7i)= -16 i+28i^2 = \color{red}{-28}\color{blue}{-16i}\)
12. \((-6+3i)+(-10-4i)= -6+3i -10-4i =\color{red}{-6-10}\color{blue}{+3i -4i}=\color{red}{-16}\color{blue}{-i}\)