Result
Enter values and select Calculate.
Method and worked example
For (a+bi)(c+di), the real part is ac−bd and imaginary part is ad+bc. Division uses the conjugate of the divisor. Magnitude is √(a²+b²), and principal argument uses atan2(b,a).
Example: (3+4i)+(1−2i)=4+2i; |3+4i|=5.
Assumptions and limitations
The argument of zero is undefined. Display values are rounded only after calculation; this is arithmetic rather than a symbolic complex-analysis system.
Calculations run in this browser. The page does not upload entered values, add them to URLs, or save them to browser storage.
Common checks
- Confirm coefficient signs and the selected mode before interpreting the result.
- Remember that interval endpoints depend on strict versus inclusive comparisons or bounds.
- Keep full precision through the method; rounded display values are for reading.
Method source
OpenStax mathematics reference. The interface and calculations are independently implemented.
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