# Complex equation z⁵ + z³ = 1

## 1 Answer

However, in this case, the given equation is a quintic equation (a polynomial of degree 5), and solving general quintic equations algebraically can be quite complex. There is no general formula for solving quintic equations using radicals, similar to quadratic or cubic equations.

Therefore, for this particular equation, it may be more practical to solve it numerically using computational methods or software, which can provide an approximate solution for z.

Dr Ali

37

Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.

- 1 Answer
- 154 views
- Pro Bono

### Related Questions

- Complex Variables Assignment 4
- Complex Numbers, Polar Form, De Moivre's Formula
- Plot real and imaginary part, modulus, phase and imaginary plane for a CFT transform given by equation on f from -4Hz to 4Hz
- Quick question regarding Analytical Applications of Differentiation
- Evaluate $\frac{1}{2 \pi i}\int_{|x|=1} \frac{z^{11}}{12z^{12}-4z^9+2z^6-4z^3+1}dz$
- Given the complex polynomial equation $z^{n} -1=0$ for n=2, 3, 4, what are the corresponding roots?
- Compute $$\oint_{|z-2|=2} \frac{\cos e^z}{z^2-4}dz$$
- Complex Variables Assignment 3

I don't think this equation can be solved analytically.