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🌐 Complex Numbers

Drag z₁ on the plane — Euler's formula, roots of unity & more

2.0
1.0
-1.0
1.5
3
z₁: 2 + i
z₂: -1 + 1.5i
Result: 1 + 2.5i
|z₁|: 2.236
arg(z₁): 26.6°
Polar:

Complex Number Plane

Euler's formula: e^(iθ) = cosθ + i·sinθ traces the unit circle. Roots of unity are the n solutions to zⁿ = 1, equally spaced on the unit circle. Multiplication multiplies magnitudes and adds angles. Drag z₁ directly on the Argand plane!