z^6-54iz^3-729=0
You asked:
Investigate the equation: \({z}^{6} - 54 i \cdot {z}^{3} - 729 = 0\).
MathBot Answer:
The 3 solutions to the equation are: \[\begin{aligned}z &= -3 i\\z &= - \frac{3 \sqrt{3}}{2} + \frac{3 i}{2} \approx -2.5980762 + 1.5 i\\z &= \frac{3 \sqrt{3}}{2} + \frac{3 i}{2} \approx 2.5980762 + 1.5 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).