What are the solutions to the equation z^4+z=0 ?

The solutions to the equation z^4+z=0 are z=0,z=-1,z= 1/2-(sqrt(3))/2 i,z= 1/2+(sqrt(3))/2 i

Find the zeros of z^4+z=0

The zeros of z^4+z=0 are z=0,z=-1,z= 1/2-(sqrt(3))/2 i,z= 1/2+(sqrt(3))/2 i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

z^{4} + z = 0

z = 0, z = - 1, z = \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} + \frac{3}{2} i

Solution steps

z^{4} + z = 0

Factor

z^{4} + z : z (z^{3} + 1)

z (z^{3} + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

z = 0 or z^{3} + 1 = 0

Solve

z^{3} + 1 = 0 : z = - 1, z = \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} + \frac{3}{2} i

The solutions are

z = 0, z = - 1, z = \frac{1}{2} - \frac{3}{2} i, z = \frac{1}{2} + \frac{3}{2} i

(1 + x)^{12} = 2.12

x^{3} = 10 - x

x, x^{4} + x^{2} y^{2} + y^{3} = 5

6 x^{5} - 12 x^{3} - 3 = 0

5 x^{3} + 8 x^{2} - 9 x + 2 = 0

What are the solutions to the equation z^4+z=0 ?
The solutions to the equation z^4+z=0 are z=0,z=-1,z= 1/2-(sqrt(3))/2 i,z= 1/2+(sqrt(3))/2 i
Find the zeros of z^4+z=0
The zeros of z^4+z=0 are z=0,z=-1,z= 1/2-(sqrt(3))/2 i,z= 1/2+(sqrt(3))/2 i