eⁱᶿ↔️cos(θ)➕`isin(θ)

#euler's formula #euler #complex analysis #trigonometry #exponential function #cosine #sine #imaginary unit #angle

ℯ^(iθ)=📈+i📉

#euler's formula #complex analysis #wave function #imaginary unit #complex plane

∮📍

#residue #complex analysis #residue theorem #singularity #integral #cauchy #pole #laurent series

ℂ📈

#complex plane #complex analysis #argand diagram #imaginary numbers #real numbers #complex numbers

🔢𝑖📈

#complex number #imaginary number #complex analysis #komplex

e`💡🥧➕1️⃣=0️⃣

#euler's identity #beautiful equation #complex analysis #five constants #pi #imaginary unit #euler's formula

⚙️🧠📈

#complex analysis #intricate systems #thorough thinking #systems thinking #detailed process

🌐(∞)

#riemann sphere #complex analysis #extended complex plane #stereographic projection #north pole infinity #compactification

ℂ→(📈=📉📈=−📉)🤝

#cauchy riemann conditions #complex analysis #complex differentiability #analytic conditions #partial derivative relations #holomorphicity test

∂u/∂x=∂v/∂y∂u/∂y=-∂v/∂x

#cauchy riemann equations #complex analysis #partial derivatives #pde #holomorphic #analytic function #complex differentiability #u_x=v_y #u_y=-v_x

🗺️🔬🤔

#detailed map #complex analysis #layers of detail #intricate information

ℂ〰️+∂⚖️⇒✨

#Looman-Menchoff theorem #complex analysis #holomorphicity #cauchy riemann equations #continuity #partial derivatives #analytic function

📐🗺️✨

#cauchy riemann equations #conformal mapping #complex analysis #analytic function #angle preservation #holomorphicity consequence #geometric interpretation

🤔🧠💡🧩

#deep thinking #mental effort #complex analysis

ℯ^(📈+i🌀)

#complex exponentiation #general complex exponential #complex analysis #real part #imaginary part

ℂ✨²

#dilogarithm #li2 #complex analysis #special function

(a+bi)→(a−bi)

#complex conjugate #complex numbers #imaginary number #complex analysis

∫🧐✨

#mathematical curve #elegant function #sophisticated graph #complex analysis #calculus symbol #data curve fancy #intellectual curve

📑📑💪😓

#heavy paperwork #thorough effort #underwriting workload #detailed processing #intensive review #complex analysis #financial stress testing