Holomorphic functions

Euler’s formula and the Cauchy-Riemann equations for complex differentiability.

Euler’s formula: e^{i theta} = cos theta + i sin theta

Euler's formula: e^{i theta} = cos theta + i sin theta

The Cauchy-Riemann equations: u_x = v_y, u_y = -v_x

The Cauchy-Riemann equations: u_x = v_y, u_y = -v_x

Wessel and Argand’s complex plane: multiplication rotates and scales

Wessel and Argand's complex plane: multiplication rotates and scales