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Simplificación de expresiones/ Descomposición de multiplicadores/ z^2+5*i*z+5*i*z^3/3

Factorizar el polinomio z^2+5*i*z+5*i*z^3/3

Expresión a simplificar:

Solución

Ha introducido [src] 
                  3
 2           5*I*z 
z  + 5*I*z + ------
               3
5iz33+(z2+5iz)\frac{5 i z^{3}}{3} + \left(z^{2} + 5 i z\right) 
z^2 + (5*i)*z + ((5*i)*z^3)/3
Descomposición de una fracción [src] 
z^2 + 5*i*z + 5*i*z^3/3
5iz33+z2+5iz\frac{5 i z^{3}}{3} + z^{2} + 5 i z 
                  3
 2           5*I*z 
z  + 5*I*z + ------
               3
Simplificación general [src] 
  /                  2\
z*\3*z + 15*I + 5*I*z /
-----------------------
           3
z(5iz2+3z+15i)3\frac{z \left(5 i z^{2} + 3 z + 15 i\right)}{3} 
z*(3*z + 15*i + 5*i*z^2)/3
Factorización [src] 
  /                _____\ /                _____\
  |      3*I   I*\/ 309 | |      3*I   I*\/ 309 |
x*|x + - --- - ---------|*|x + - --- + ---------|
  \       10       10   / \       10       10   /
x(x+(−309i10−3i10))(x+(−3i10+309i10))x \left(x + \left(- \frac{\sqrt{309} i}{10} - \frac{3 i}{10}\right)\right) \left(x + \left(- \frac{3 i}{10} + \frac{\sqrt{309} i}{10}\right)\right) 
(x*(x - 3*i/10 - i*sqrt(309)/10))*(x - 3*i/10 + i*sqrt(309)/10)
Unión de expresiones racionales [src] 
  /                  2\
z*\3*z + 15*I + 5*I*z /
-----------------------
           3
z(5iz2+3z+15i)3\frac{z \left(5 i z^{2} + 3 z + 15 i\right)}{3} 
z*(3*z + 15*i + 5*i*z^2)/3
Compilar la expresión [src] 
                  3
 2           5*I*z 
z  + 5*I*z + ------
               3
5iz33+z2+5iz\frac{5 i z^{3}}{3} + z^{2} + 5 i z 
       /         3\
 2     |      5*z |
z  + I*|5*z + ----|
       \       3  /
z2+i(5z33+5z)z^{2} + i \left(\frac{5 z^{3}}{3} + 5 z\right) 
z^2 + i*(5*z + 5*z^3/3)
Respuesta numérica [src] 
z^2 + 5.0*i*z + 1.66666666666667*i*z^3
z^2 + 5.0*i*z + 1.66666666666667*i*z^3
Potencias [src] 
                  3
 2           5*I*z 
z  + 5*I*z + ------
               3
5iz33+z2+5iz\frac{5 i z^{3}}{3} + z^{2} + 5 i z 
z^2 + 5*i*z + 5*i*z^3/3
Parte trigonométrica [src] 
                  3
 2           5*I*z 
z  + 5*I*z + ------
               3
5iz33+z2+5iz\frac{5 i z^{3}}{3} + z^{2} + 5 i z 
z^2 + 5*i*z + 5*i*z^3/3
Denominador común [src] 
                  3
 2           5*I*z 
z  + 5*I*z + ------
               3
5iz33+z2+5iz\frac{5 i z^{3}}{3} + z^{2} + 5 i z 
z^2 + 5*i*z + 5*i*z^3/3
Denominador racional [src] 
   2        3         
3*z  + 5*I*z  + 15*I*z
----------------------
          3
5iz3+3z2+15iz3\frac{5 i z^{3} + 3 z^{2} + 15 i z}{3} 
(3*z^2 + 5*i*z^3 + 15*i*z)/3
Combinatoria [src] 
  /                  2\
z*\3*z + 15*I + 5*I*z /
-----------------------
           3
z(5iz2+3z+15i)3\frac{z \left(5 i z^{2} + 3 z + 15 i\right)}{3} 
z*(3*z + 15*i + 5*i*z^2)/3
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