Euler's formula · 羊·實驗

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One rotation, read as complex multiplication, a point on the unit circle, and the cosine and sine of the same angle.

The same addition of arguments shows up in a product, in an nth power, and in n equal roots.

Any nonzero complex number is written as z = re^(iθ), with modulus r and argument θ, linking rectangular and polar coordinates.

Euler's formula e^(iθ) = cos θ + i sin θ rotates a vector on the complex plane and traces the sine wave of its imaginary part.

Drag a complex number z and watch a power multiply the argument by n, or roots divide the circle into n equal parts.