Complex Number to Polar Form
Complex Number to Polar Form: calculate results from explicit inputs, with a formula and worked example.
Formula
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Zero has no unique argument.
Example Calculation
- Real part a: 3
- Imaginary part b: 4
3+4i has magnitude 5 and argument approximately 53.1301°.
Method references
Frequently asked questions
How do I use this calculator?
Enter real part a, imaginary part b. The result updates automatically. Use Reset to restore the example values.
What method does it use?
r = √(a²+b²); θ = atan2(b,a); z = r(cos θ+i sin θ). Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Zero has no unique argument.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.