Sr Examen
Factorizar el polinomio z^2+5*i*z+5*i*z^3/3
Solución
Ha introducido
[src]
3
2 5*I*z
z + 5*I*z + ------
3
$$\frac{5 i z^{3}}{3} + \left(z^{2} + 5 i z\right)$$
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
$$\frac{5 i z^{3}}{3} + z^{2} + 5 i z$$
3
2 5*I*z
z + 5*I*z + ------
3
Simplificación general
[src]
/ 2\
z*\3*z + 15*I + 5*I*z /
-----------------------
3
$$\frac{z \left(5 i z^{2} + 3 z + 15 i\right)}{3}$$
z*(3*z + 15*i + 5*i*z^2)/3
Factorización
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/ _____\ / _____\ | 3*I I*\/ 309 | | 3*I I*\/ 309 | x*|x + - --- - ---------|*|x + - --- + ---------| \ 10 10 / \ 10 10 /
$$x \left(x + \left(- \frac{\sqrt{309} i}{10} - \frac{3 i}{10}\right)\right) \left(x + \left(- \frac{3 i}{10} + \frac{\sqrt{309} i}{10}\right)\right)$$
(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
$$\frac{z \left(5 i z^{2} + 3 z + 15 i\right)}{3}$$
z*(3*z + 15*i + 5*i*z^2)/3
Compilar la expresión
[src]
3
2 5*I*z
z + 5*I*z + ------
3
$$\frac{5 i z^{3}}{3} + z^{2} + 5 i z$$
/ 3\
2 | 5*z |
z + I*|5*z + ----|
\ 3 /
$$z^{2} + i \left(\frac{5 z^{3}}{3} + 5 z\right)$$
z^2 + i*(5*z + 5*z^3/3)
Respuesta numérica
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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
$$\frac{5 i z^{3}}{3} + z^{2} + 5 i z$$
z^2 + 5*i*z + 5*i*z^3/3
Parte trigonométrica
[src]
3
2 5*I*z
z + 5*I*z + ------
3
$$\frac{5 i z^{3}}{3} + z^{2} + 5 i z$$
z^2 + 5*i*z + 5*i*z^3/3
Denominador común
[src]
3
2 5*I*z
z + 5*I*z + ------
3
$$\frac{5 i z^{3}}{3} + z^{2} + 5 i z$$
z^2 + 5*i*z + 5*i*z^3/3
Denominador racional
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2 3
3*z + 5*I*z + 15*I*z
----------------------
3
$$\frac{5 i z^{3} + 3 z^{2} + 15 i z}{3}$$
(3*z^2 + 5*i*z^3 + 15*i*z)/3
Combinatoria
[src]
/ 2\
z*\3*z + 15*I + 5*I*z /
-----------------------
3
$$\frac{z \left(5 i z^{2} + 3 z + 15 i\right)}{3}$$
z*(3*z + 15*i + 5*i*z^2)/3