Best way to convert complex numbers, rect, polar, euler

[Joe Horn]

It's built in. Press the angle [∡] key (Shift ×) to toggle any result between rectangular and polar notation. The angle will be interpreted according to the current angle mode, of course.

Example:
3+4i Enter --> 3+4*i
[∡] --> 5 ∡ 0.9273 (radian mode)

1∡2 Enter --> 1∡2 (radian mode)
[∡] --> -0.4161+0.9093*i

You can also use (x,y) notation instead of x+yi notation for inputs, and in Home Settings you can select whether you want outputs to be in (x,y) or x+yi notation.

The programmable functions polar_coordinates and rectangular_coordinates are also available. See their help screens for more info.