Visualizations · Mathematics
Complex plane, operations and geometry
Displaying complex numbers
Geometry of addition in complex plane
|z| = distance from origin
Angle of complex number in plane
z̄ = reflection over real axis
Rotation and scaling in the plane
Geometry of complex division
z = r·e^(iθ) - polar coordinates
e^z in the complex plane
1/z - inversion in complex plane
az + b in the complex plane
i, i², i³, i⁴ = 1, cyclically
e^(iπ) + 1 = 0
(cosθ + i·sinθ)ⁿ = cos(nθ) + i·sin(nθ)
n solutions of zⁿ = 1
Roots of any complex number
Fractal from complex iteration
Solving zⁿ = a and the regular polygon of roots