Drag z in the left plane; the right plane draws the spiral of partial products (1 + z/n)ⁿ for n = 1024, and readouts compare the measured length and angle to eᵃ and b.
The claim above is what this widget demonstrates. Disagree with it?
For z = a + bi, e^z has length eᵃ and angle b radians, as the partial products of (1 + z/n)ⁿ show.
Builds on Euler's chain. Taught in Parameterization and substitution.
Drag z in the left plane; the right plane draws the spiral of partial products (1 + z/n)ⁿ for n = 1024, and readouts compare the measured length and angle to eᵃ and b.
The claim above is what this widget demonstrates. Disagree with it?