MathProblemsBank

10.6.27 Analytic Functions

Condition: present a given function \ (\ omega = f (z) \), where \ (z = x+i y \), in the form \ (\ omega = u (x, y)+i v (x, y) \); Check if it is analytical. If so, then find the value of its derivative at a given point \ (z_ {0} \). \ [\ omega = e^{-z^{2}}, \ quad z_ {0} = i \]

Differentiation of Analytic Functions, Finding Their Real and Imaginary Parts, Finding the Number of Roots Equates Using the Argement Principle, Roucher's Theorem and Much More in this space.