Find Complex Root of z^5=0 | Math Solutions

[Amer]

how to find the complex root of

$$z^5 = 0$$ there is one real root 0

 

[Evgeny.Makarov]

This equation has a single complex root, i.e., 0.

 

[Dustinsfl]

This equation has a single complex root, i.e., 0.

with a multiplicity of 5.

 

[Amer]

thanks

 

[blue_raver22]

and four complex roots, 0+0i, 0+0i, 0+0i, 0+0i

I would like to clarify that the statement "0+0i" does not refer to a complex root. A complex number is composed of a real and an imaginary part, and the imaginary part is represented by the letter "i". Therefore, the complex roots of z^5=0 would be 0+0i, 0+0i, 0+0i, 0+0i, and 0+0i. These roots can also be written as 0, 0i, 0i, 0i, and 0i, respectively.

To find the complex roots of z^5=0, we can use the fact that any complex number can be written in polar form as r(cosθ + isinθ), where r is the magnitude and θ is the angle in the complex plane. In this case, since the equation is equal to 0, the magnitude r must be equal to 0. This means that all the complex roots will have a magnitude of 0.

To find the angles θ, we can use the fact that the equation can also be written as z^5=0+0i. Therefore, the angle θ for each root can be found by taking the argument of 0+0i, which is any angle between 0 and 2π. This gives us the complex roots 0(cosθ + isinθ), where θ can take any value between 0 and 2π.

In conclusion, the complex roots of z^5=0 are 0, 0i, 0i, 0i, and 0i. These roots can also be written in polar form as 0(cosθ + isinθ), where θ can take any value between 0 and 2π.