I'm afraid I didn't follow. What did you mean with 2CIS(40) * 2CIS(22) = 1CIS(30) + 2CIS(33)? Let's take some specific examples: if

and

, we have that:

.

We see that

or 120 degrees. Notice that

and

, and so

.

The underlying thought is this: a complex number can be represented by a vector starting at the origin, and thus he has an angle within

. When you multiply two complex numbers, the result will always sum the angles and their magnitudes will be multiplied.

In our case, if instead of

and

we had

and

, the result would be

, showing that magnitudes multiplied, however the sum is unchanged.

I hope this clarified it further.