Determine the argument of the complex $Z$
Solution 1:
Since $e^{-2ix}$ and $e^{6ix}$ are of equal magnitude, they form two adjacent sides of a rhombus and the sum's argument is the average of those of its components: $\frac{-2x+6x}2=2x$.
Since $e^{-2ix}$ and $e^{6ix}$ are of equal magnitude, they form two adjacent sides of a rhombus and the sum's argument is the average of those of its components: $\frac{-2x+6x}2=2x$.