10.3.35 Operations with complex numbers
Condition: Three complex numbers \( z_{1}, z_{2}, z_{3} \) are given. Calculate \( z \) in algebraic form. \[ \begin{array}{l} z=\frac{z_{1}+2 z_{3}}{z_{2}}, \quad z_{1}=2+3 i, \quad z_{2}=1+2 i, \\ z_{3}=-2+3 i . \end{array}\]
Operations with complex numbers, their algebraic, trigonometric and exponential forms. Derivatives of functions, finding complex roots of polynomials, solving equations in complex numbers.