(z+1)^3+z^3=0
You asked:
Solve the equation \({\left( z + 1 \right)}^{3} + {z}^{3} = 0\) for the variable \(z\).
MathBot Answer:
The 3 solutions to the equation are: \[\begin{aligned}z &= - \frac{1}{2} = -0.5\\z &= - \frac{1}{2} - \frac{\sqrt{3} i}{2} \approx -0.5 -0.8660254 i\\z &= - \frac{1}{2} + \frac{\sqrt{3} i}{2} \approx -0.5 + 0.8660254 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).