Linked from

The 25 pages that link to Euler's formula, each with the reason it gives.

• Leonhard EulerBroader topic: This formula made complex numbers a powerful language for periodic phenomena.

• Complex numberRelated: It expresses unit-length complex numbers as rotations around the origin.

• Complex planeRelated: It connects angular position on the plane with exponential notation.

• SineRelated: It expresses sine through the exponential function of an imaginary argument.

• Trigonometric functionsRelated: It combines sine and cosine into complex exponentials and simplifies many calculations.

• Complex exponentialBroader topic: It states precisely how imaginary inputs produce circular motion.

• Unit circleRelated: It encodes each unit-circle point as a complex exponential.

• PhasorRelated: It converts a sinusoid into a rotating complex exponential, the basis of phasor notation.

• Root of unityRelated: It expresses each complex root of unity as an angle on the unit circle.

• Complex logarithmRelated: It shows that changing an angle by \(2\pi\) leaves the exponential unchanged.

• CosineRelated: It packages cosine and sine into one expression using complex numbers.

• Fast Fourier transformRelated: It connects the FFT's complex multiplications to sinusoidal oscillations.

• Complex multiplicationRelated: It expresses complex factors as rotations, making angle addition in products explicit.

• Imaginary unitRelated: Setting x to π/2 expresses i as a complex exponential.

• Euler's identityNarrower topic: Setting x to π gives e^{iπ} = −1, the central step behind the identity.

• Euler's NumberRelated: It extends the exponential built from e into the complex plane.

• Hyperbolic functionsRelated: Replacing the imaginary angle with a real argument links trigonometric and hyperbolic definitions.

• Trigonometric identityRelated: It compresses many trigonometric identities into algebra with complex exponentials.

• Algebraic identityRelated: It is a celebrated identity connecting exponential and trigonometric expressions.

• Polar formRelated: It gives the exponential form re^{iθ} of the same representation.

• Fresnel integralsRelated: It combines the sine and cosine integrals into one complex-valued function.

• De Moivre's formulaRelated: It rewrites the trigonometric expression as an exponential, making the power rule immediate.

• Sine and cosineRelated: It packages sine and cosine together and makes angle addition and oscillation easier to analyze.

• Pythagorean trigonometric identityRelated: Its unit-modulus consequence gives another route to the sine-cosine identity.

• Imaginary numberRelated: It places imaginary multiples of i inside complex exponentials.