Trigonometric functions (used in the trigonometric form of a complex number) are 
-periodic, which means that for any arguments differing by, say, 
they assume the same value.
For example:
So, for instance, a complex number in its trigonometric form:
This is the same complex number as:
because the arguments of the trigonometric functions differ by .
What arguments should be used in the trigonometric form of a complex number?
What arguments are conventionally used? In Poland (and in my course on complex numbers) from the interval 
. However, in older textbooks or foreign ones, it might be from the interval 
. It’s important to keep this in mind when verifying your calculations against textbook answers.
