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Simplificación de expresiones/ Descomposición en fracciones simples/ (i^7*(3-4i)/(1-i)^2)+((2i-1)/((3-i)*(1-i)^2))

¿Cómo vas a descomponer esta (i^7*(3-4i)/(1-i)^2)+((2i-1)/((3-i)*(1-i)^2)) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 7                             
I *(3 - 4*I)       2*I - 1     
------------ + ----------------
         2                    2
  (1 - I)      (3 - I)*(1 - I)
$$\frac{i^{7} \left(3 - 4 i\right)}{\left(1 - i\right)^{2}} + \frac{-1 + 2 i}{\left(1 - i\right)^{2} \left(3 - i\right)}$$ 
(i^7*(3 - 4*i))/(1 - i)^2 + (2*i - 1)/(((3 - i)*(1 - i)^2))
Simplificación general [src] 
5   9*I
- - ---
4    4
$$\frac{5}{4} - \frac{9 i}{4}$$ 
5/4 - 9*i/4
Respuesta numérica [src] 
1.25 - 2.25*i
1.25 - 2.25*i
Abrimos la expresión [src] 
 7                              
I *(3 - 4*I)   (3 + I)*(2*I - 1)
------------ + -----------------
         2                  2   
  (1 - I)         10*(1 - I)
$$\frac{i^{7} \left(3 - 4 i\right)}{\left(1 - i\right)^{2}} + \frac{\left(-1 + 2 i\right) \left(3 + i\right)}{10 \left(1 - i\right)^{2}}$$ 
(i^7*(3 - 4*i))/(1 - i)^2 + (3 + i)*(2*i - 1)/(10*(1 - i)^2)
Compilar la expresión [src] 
  I*(3 - 4*I)   (-1 + 2*I)*(3 + I)
- ----------- + ------------------
           2                 2    
    (1 - I)        10*(1 - I)
$$- \frac{i \left(3 - 4 i\right)}{\left(1 - i\right)^{2}} + \frac{\left(-1 + 2 i\right) \left(3 + i\right)}{10 \left(1 - i\right)^{2}}$$ 
-i*(3 - 4*i)/(1 - i)^2 + (-1 + 2*i)*(3 + i)/(10*(1 - i)^2)
Denominador racional [src] 
        4        2           
-(1 + I) *(1 - I) *(9 + 5*I) 
-----------------------------
              32
$$- \frac{\left(1 - i\right)^{2} \left(1 + i\right)^{4} \left(9 + 5 i\right)}{32}$$ 
-(1 + i)^4*(1 - i)^2*(9 + 5*i)/32
Denominador común [src] 
-I*(9 + 5*I) 
-------------
      4
$$- \frac{i \left(9 + 5 i\right)}{4}$$ 
-i*(9 + 5*i)/4
Unión de expresiones racionales [src] 
(-1 + 2*I)*(3 + I) - 10*I*(3 - 4*I)
-----------------------------------
                      2            
            10*(1 - I)
$$\frac{- 10 i \left(3 - 4 i\right) + \left(-1 + 2 i\right) \left(3 + i\right)}{10 \left(1 - i\right)^{2}}$$ 
((-1 + 2*i)*(3 + i) - 10*i*(3 - 4*i))/(10*(1 - i)^2)
Potencias [src] 
                          /3    I \
               (-1 + 2*I)*|-- + --|
I*(-3 + 4*I)              \10   10/
------------ + --------------------
         2                  2      
  (1 - I)            (1 - I)
$$\frac{i \left(-3 + 4 i\right)}{\left(1 - i\right)^{2}} + \frac{\left(-1 + 2 i\right) \left(\frac{3}{10} + \frac{i}{10}\right)}{\left(1 - i\right)^{2}}$$ 
  I*(3 - 4*I)   (-1 + 2*I)*(3 + I)
- ----------- + ------------------
           2                 2    
    (1 - I)        10*(1 - I)
$$- \frac{i \left(3 - 4 i\right)}{\left(1 - i\right)^{2}} + \frac{\left(-1 + 2 i\right) \left(3 + i\right)}{10 \left(1 - i\right)^{2}}$$ 
-i*(3 - 4*i)/(1 - i)^2 + (-1 + 2*i)*(3 + i)/(10*(1 - i)^2)
Combinatoria [src] 
-(9 + 5*I) 
-----------
          2
2*(-1 + I)
$$- \frac{9 + 5 i}{2 \left(-1 + i\right)^{2}}$$ 
-(9 + 5*i)/(2*(-1 + i)^2)
Parte trigonométrica [src] 
  I*(3 - 4*I)   (-1 + 2*I)*(3 + I)
- ----------- + ------------------
           2                 2    
    (1 - I)        10*(1 - I)
$$- \frac{i \left(3 - 4 i\right)}{\left(1 - i\right)^{2}} + \frac{\left(-1 + 2 i\right) \left(3 + i\right)}{10 \left(1 - i\right)^{2}}$$ 
-i*(3 - 4*i)/(1 - i)^2 + (-1 + 2*i)*(3 + i)/(10*(1 - i)^2)
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