Complex Number Calculator is designed for the exact search intent behind “complex number calculator”. Calculate arithmetic with complex numbers in a + bi form and show the rule used for each operation. Calculate arithmetic with complex numbers in a + bi form and show the rule used for each operation. Add/subtract Combine real parts and imaginary parts separately. Multiply (a+bi)(c+di)=(ac−bd)+(ad+bc)i . Divide Multiply numerator and denominator by the denominator's complex conjugate; division by 0+0i is undefined. Worked example: (2+3i)(4−i) = 11+10i. Common practical uses include Check algebra work; Solve engineering calculations; Practice complex arithmetic; Verify conjugate-based division. Important limitations: Division by zero is undefined. Formatting/rounding can hide exact values. Advanced functions require separate functionality. Key questions this page should answer include: What is a complex number? A number written as a+bi where i²=−1. How do I add complex numbers? Add real parts together and imaginary parts together. How do I multiply them? Distribute terms and use i²=−1. What is a complex conjugate? For a+bi, the conjugate is a−bi. Can I divide by 0+0i? No. The page should stay focused on this differentiator: Cover the four core arithmetic operations with exact algebraic rules. The tool should appear before the explanatory copy so a visitor can complete the task immediately, then use the supporting content to verify the method and understand the result. The explanation should keep terminology consistent with the calculator or converter interface, because a mismatch between labels in the tool and labels in the content can create confusion and weaken search-intent alignment. Where the calculation or transformation has edge cases, the page should state them directly instead of implying that every input is valid. The worked example should mirror the real inputs accepted by the tool and show enough arithmetic or transformation logic for the result to be independently checked. Related internal links should connect to genuinely adjacent tasks rather than broad category pages, helping users continue the workflow without creating unnecessary keyword overlap.
How to use this tool
Add/subtract
Combine real parts and imaginary parts separately.
Multiply
(a+bi)(c+di)=(ac−bd)+(ad+bc)i.
Divide
Multiply numerator and denominator by the denominator's complex conjugate; division by 0+0i is undefined.
Examples
Example
(2+3i)(4−i) = 11+10i.
Common use cases
- Check algebra work
- Solve engineering calculations
- Practice complex arithmetic
- Verify conjugate-based division
Frequently asked questions
What is a complex number?
A number written as a+bi where i²=−1.
How do I add complex numbers?
Add real parts together and imaginary parts together.
How do I multiply them?
Distribute terms and use i²=−1.
What is a complex conjugate?
For a+bi, the conjugate is a−bi.
Can I divide by 0+0i?
No.