Dots

There is a definite difference between what these dots represent. The

red - on the complex plane - sits squarely on pi/3, with a cos value of .5,

and a i*sin value of .866. The grey dot is a polar complex with a modulus

(length) of 7.3303

The green dot is also at ,5 for x but the imaginary value is at 7.3303.

This is also a complex number, but will have different cos and sin readings

from the others.

 7.3303 equals (app) .866 + 2 pi.

*     *     *

Two pi multiple angles on the sin element will keep signs the same,

which is neat. But calculations for the real term will take the cos of the

sin!😕

source: Math is Fun

i*sin assigns it's angle value to the cos calculation as well.