10.3.36 Operations with complex numbers
Condition: Three complex numbers \( z_{1}, z_{2}, z_{3} \) are given. Calculate \( z \) in algebraic form. \[ \begin{array}{l} z=\frac{z_{2}}{z_{1}}+3 i z, \\ z_{1}=1+3 i, \quad z_{2}=4+2 i, \quad z_{3}=-4+2 i . \end{array}\]
Operations with complex numbers, their algebraic, trigonometric and exponential forms. Derivatives of functions, finding complex roots of polynomials, solving equations in complex numbers.