Combine real and imaginary parts with guided calculations. See polar values, conjugates, and simplified forms. Download reports and learn every step with confidence today.
Use rectangular form only. Enter at least two numbers. Blank cards are ignored automatically.
This sample shows how separate real and imaginary parts combine into one final sum.
| Complex number | Real part | Imaginary part | Rectangular form |
|---|---|---|---|
| z1 | 3 | 4 | 3 + 4i |
| z2 | -1 | 5 | -1 + 5i |
| z3 | 6 | -2 | 6 - 2i |
| Total | 8 | 7 | 8 + 7i |
Example result: (3 + 4i) + (-1 + 5i) + (6 - 2i) = 8 + 7i
For complex numbers written as zk = ak + bki, the total sum is found by adding all real parts together and all imaginary parts together.
z = (a1 + b1i) + (a2 + b2i) + ... + (an + bni) z = (a1 + a2 + ... + an) + (b1 + b2 + ... + bn)i |z| = √(x² + y²) arg(z) = atan2(y, x) conjugate(z) = x - yiHere, x is the final real total and y is the final imaginary total. This calculator also reports modulus, argument, polar form, and conjugate of the sum.
It adds complex numbers written in rectangular form, where each number has a real part and an imaginary part. The tool combines matching parts and returns the final sum, modulus, argument, conjugate, and polar form.
Complex addition is performed by adding all real parts together and all imaginary parts together. The result remains a complex number in the form x + yi.
Yes. Negative real parts and negative imaginary parts are fully supported. This is useful for subtraction effects, direction changes, or algebraic expressions containing signed values.
These values help you understand the magnitude and direction of the final complex sum. They are especially useful when converting rectangular results into polar form or analyzing phasors.
The conjugate keeps the real part unchanged and flips the sign of the imaginary part. If the sum is x + yi, its conjugate is x - yi.
No. Only the cards containing values are used. You need at least two complex numbers for addition, while any remaining blank cards are ignored during calculation.
Yes. You can enter integers or decimal numbers in any real or imaginary field. The output is formatted cleanly while keeping suitable precision for most classroom and practical tasks.
Use CSV when you need spreadsheet analysis or records. Use PDF when you want a printable summary, shareable report, or a clean reference for homework and documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.