z^2-3z+2i=0
You asked:
Investigate the equation: \({z}^{2} - 3 z + 2 i = 0\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}z &= \frac{3}{2} + \frac{\sqrt[4]{145} \cos{\left(\frac{\arctan{\left(\frac{8}{9} \right)}}{2} \right)}}{2} - \frac{\sqrt[4]{145} i \sin{\left(\frac{\arctan{\left(\frac{8}{9} \right)}}{2} \right)}}{2} \approx 3.1217889 -0.61660305 i\\z &= - \frac{\sqrt[4]{145} \cos{\left(\frac{\arctan{\left(\frac{8}{9} \right)}}{2} \right)}}{2} + \frac{3}{2} + \frac{\sqrt[4]{145} i \sin{\left(\frac{\arctan{\left(\frac{8}{9} \right)}}{2} \right)}}{2} \approx -0.12178893 + 0.61660305 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).