Complex analysis: Exp, log, sin, cos
This lecture is part of an online undergraduate course on complex analys We show how to extend the elementary transcendental functions (exp, log, sin, cos, and so on) to complex numbers. In particular we describe Euler's discovery that exponential and trigonometric functions are essentially the same, and give some applications. For the other lectures in the course see • Complex analysis

▶︎
Complex analysis: Holomorphic functions

▶︎
Complex analysis: Roots

▶︎
Complex Logarithm, Branch Points, and Branch Cuts

▶︎
Solving sin(x)^sin(x)=2

▶︎
Complex analysis: Harmonic functions

▶︎
Complex analysis: Integration

▶︎
What are complex numbers? | Essence of complex analysis #2

▶︎
Complex analysis: Elliptic functions

▶︎
Indeterminate: the hidden power of 0 divided by 0

▶︎
Complex Analysis L04: The Complex Logarithm, Log(z)

▶︎
William Dunham, A tribute to Euler

▶︎
The most beautiful formula not enough people understand

▶︎
Complex number fundamentals | Ep. 3 Lockdown live math

▶︎
We're 99.9% sure this pattern is true, but no one can prove it

▶︎
Complex analysis: Residue calculus

▶︎
Complex analysis: Arithmetic

▶︎
can we have sin(i)?

▶︎
The Riemann Hypothesis, Explained

▶︎
