Drag the point z on the Argand diagram to see its modulus and argument. Then switch to the 3D view and watch the same point spiral round as θ sweeps — its shadow on one wall traces a cosine wave, its shadow on the other traces a sine wave.
Select the point z and drag it to any position
z = r(cosθ + i sinθ) as θ sweeps round
Point z
Drag z on the diagram, or set r and θ directly.
Try these
3D animation
The maths
x and y are just the coordinates of z: the Real and Imaginary parts. Euler's formula says exactly how they relate to r and θ.
arg(z) is given in (−180°, 180°] — negative just means z sits below the Real axis, measured clockwise instead of anticlockwise.