65FC. Funciones Complejas - JulTob/Mathematics GitHub Wiki

The starting point of our study is the idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex.

𝑓 ∶ ℂ⟶ℂ

ℂ ≃ ℝ² = ℝ⨯ℝ

𝑧 = (𝑥,𝑦)= 𝑥 + 𝚒𝑦 = 𝑥⊥𝑦 = 𝚛_{⊾𝜃} ∈ℂ 

A complex function that is differentiable in a complex wayis called holomorphicity.

\displaystyle \lim_{h \to 0} \frac{𝑓(𝑧+∆𝑧)-𝑓(𝑧)}{∆𝑧}

With ∆𝑧 allowing complex values.