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The Euler's Identity is considered to be the most beautiful equation in math, which says e^(i*pi)+1=0, tshirt here: https://amzn.to/427Seae This video is for calculus 2 students after we cover the Taylor series. We will first do the classic proof of Euler's formula where we use the Taylor series of e^x, sin(x), cos(x), and complex numbers to draw the connection that e^(iz)=cos(z)+isin(z). Then we will plug in pi and get the equation e^(i*pi)=1, which is the same as e^(i*pi)+1=0. Euler's formula is also the main building block of complex analysis.

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See how we can integrate e^(ax)*sin(bx) with Euler's formula and no integration by parts:    • Integral of e^(ax)sin(bx) by using co...  

0:00 Proving Euler's Formula e^(iθ)=cos(θ)+i*sin(θ)
4:58 Check out Brilliant
5:52 Proving Euler's Identity e^(i*pi)+1=0

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Calculus 2 power series pdf: https://bit.ly/calc2series'>https://bit.ly/calc2series