Euler’s formula (HSC SSCE Mathematics Extension 2): Flashcards

e^{iθ} = cosθ + i sinθ

It connects trigonometric and exponential functions.

e^{iθ} represents exponential increase with imaginary exponent.

e^{ix} = cos(x) + i sin(x) for any real x.

Taylor series for e^x, sin x, and cos x.

z = re^{iθ} for any complex number z.

It becomes addition: e^{iθ} * e^{iφ} = e^{i(θ+φ)}.

A point on the unit circle in the Argand plane.

(cos θ + i sin θ)^n = cos(nθ) + i sin(nθ).

It helps derive the theorem using (e^{iθ})^n.