Basisbewerkingen gemengd (a+bi)

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Bereken

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

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Bereken

Verbetersleutel

1. \(\frac{2+8i}{4-10i}= \frac{2+8i}{4-10i} \cdot \frac{4+10i}{4+10i} = \frac{8+20i +32 i+80i^2 }{(4)^2-(-10i)^2} = \frac{8+20i +32 i-80}{16 + 100} = \frac{-72+52i }{116} = \frac{-18}{29} - \frac{-13}{29}i \)
2. \(\frac{9-8i}{3+6i}= \frac{9-8i}{3+6i} \cdot \frac{3-6i}{3-6i} = \frac{27-54i -24 i+48i^2 }{(3)^2-(6i)^2} = \frac{27-54i -24 i-48}{9 + 36} = \frac{-21-78i }{45} = \frac{-7}{15} + \frac{-26}{15}i \)
3. \((-7-i)+(2-9i)= -7-i +2-9i =\color{red}{-7+2}\color{blue}{-i -9i}=\color{red}{-5}\color{blue}{-10i}\)
4. \((-10i) \cdot (10+7i)= -100 i-70i^2 = \color{red}{70}\color{blue}{-100i}\)
5. \((-1-7i) \cdot (1-8i)= -1+8i -7 i+56i^2 = -1+8i -7 i-56= \color{red}{-1-56}\color{blue}{+8i -7i}=\color{red}{-57}\color{blue}{+i}\)
6. \(\frac{9-2i}{1+5i}= \frac{9-2i}{1+5i} \cdot \frac{1-5i}{1-5i} = \frac{9-45i -2 i+10i^2 }{(1)^2-(5i)^2} = \frac{9-45i -2 i-10}{1 + 25} = \frac{-1-47i }{26} = \frac{-1}{26} + \frac{-47}{26}i \)
7. \(\frac{-2+9i}{5+7i}= \frac{-2+9i}{5+7i} \cdot \frac{5-7i}{5-7i} = \frac{-10+14i +45 i-63i^2 }{(5)^2-(7i)^2} = \frac{-10+14i +45 i+63}{25 + 49} = \frac{53+59i }{74} = \frac{53}{74} - \frac{-59}{74}i \)
8. \((-9+8i) \cdot (-5-3i)= 45+27i -40 i-24i^2 = 45+27i -40 i+24= \color{red}{45+24}\color{blue}{+27i -40i}=\color{red}{69}\color{blue}{-13i}\)
9. \((-5+2i)+(-2+9i)= -5+2i -2+9i =\color{red}{-5-2}\color{blue}{+2i +9i}=\color{red}{-7}\color{blue}{+11i}\)
10. \((-1+9i)-(4-6i)= -1+9i -4+6i =\color{red}{-1-4}\color{blue}{+9i +6i}=\color{red}{-5}\color{blue}{+15i}\)
11. \((-10-9i)+(1-6i)= -10-9i +1-6i =\color{red}{-10+1}\color{blue}{-9i -6i}=\color{red}{-9}\color{blue}{-15i}\)
12. \((2-4i)+(1-3i)= 2-4i +1-3i =\color{red}{2+1}\color{blue}{-4i -3i}=\color{red}{3}\color{blue}{-7i}\)