Complex nth Roots Calculator
Complex nth Roots: 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. Lists all roots; zero has one distinct root.
Example Calculation
- Real part: 1
- Imaginary part: 0
- Root index n: 3
The cube roots of 1 are 1 and −½ ± (√3/2)i.
Method references
Frequently asked questions
How do I use this calculator?
Enter real part, imaginary part, root index n. The result updates automatically. Use Reset to restore the example values.
What method does it use?
roots = |z|^(1/n) [cos((arg z+2πk)/n)+i sin((arg z+2πk)/n)], k=0…n−1. Real finite inputs. Numeric results use floating-point arithmetic; this is not a symbolic computer algebra system. Lists all roots; zero has one distinct root.
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.