The trigonometric form of a complex number is unique - true or false?

Answer with explanation:

let, Z= a + i b,be a complex number.

Where, a = r cos A

 b= r sin A

Now, if we replace A, by, 2 kπ + A,in the above equation,where k is any positive integer,beginning from ,0.k=0,1,2,3,4,....

So, for different value of , k ,there will be Different Complex number.

→So,the Statement: The trigonometric form of a complex number is unique = False

because they could drop even lower..