When to use this calculator
Find a complex number’s direction in the complex plane. Returns a principal angle from −180° to 180°. The zero complex number has no defined argument.
Explore the algebra & number calculators for other questions in this topic. For a related calculation, use the Complex Number Magnitude Calculator: Find the magnitude of a complex number from its real and imaginary components.
PUTTING IT INTO PRACTICE
Complex Number Argument: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Real part | 0 |
| Imaginary part | 1 |
| Result | 90 degrees |
- Check the input labels and enter the example values above.
- Apply the relationship: Argument = atan2(imaginary,real) × 180/π.
- The result is 90 degrees, rounded for display.
How to interpret your result
Returns a principal angle from −180° to 180°. The zero complex number has no defined argument.
Identify whether the question asks for one term, a total or a count of possible selections. Sequences use a fixed difference or ratio. In counting problems, order and replacement determine the correct model.
Frequently asked questions
Do combinations and permutations count the same thing?
No. Combinations ignore the order of selection; permutations count different orders separately.
When is the complex number argument calculator useful?
Find a complex number’s direction in the complex plane. Returns a principal angle from −180° to 180°. The zero complex number has no defined argument.
How do I use the complex number argument calculator?
Enter real part, imaginary part. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Argument = atan2(imaginary,real) × 180/π.
What should I check before using the result?
Returns a principal angle from −180° to 180°. The zero complex number has no defined argument.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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