What is Euler's formula actually saying? | Ep. 4 Lockdown live math

Summary by Krater

This video explores Euler's formula and the exponential function in the complex plane, explaining how the formula relates to rotation and complex numbers through geometric visualization and infinite polynomials.

From the video

Answers: What is Euler's formula and how does it work in the complex plane?

• Euler's formula
• Complex plane
• Exponential function expansion
• Unit circle rotation
• Powers of i

What it concludes

• Euler's formula links exponential growth with rotation around the unit circle.
• The exponential function can be represented as an infinite polynomial series.
• Multiplying by the imaginary unit i corresponds to a 90-degree rotation in the complex plane.