Trigonometric form of a complex number – different angles, same solution?

Krystian Karczyński

Founder and General Manager of eTrapez.

Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.

He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.

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.

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