10.3.25 Operations with complex numbers
Condition: Shade in the figure the area in the plane \(Z, \quad \) defined by the inequalities. The boundaries of the region that belongs to it are drawn with solid lines, those that do not belong to dotted lines. \[ \begin{array}{l} 0 \leq|z+\sqrt{2}|-|z-\sqrt{2}| \leq 2 \\ |z+\sqrt{3}|+|z-\sqrt{3}|<4 \end{array} \]
Operations with complex numbers, their algebraic, trigonometric and exponential forms. Derivatives of functions, finding complex roots of polynomials, solving equations in complex numbers.