Complex numbers look intimidating with their imaginary parts, but adding them is one of the friendliest operations in all of math — simpler, honestly, than adding fractions. A complex number like 3 + 4i has two independent pieces, the real part (3) and the imaginary part (4i), and addition just handles each piece separately: add the reals together, add the imaginaries together, done. So (3 + 4i) + (1 - 2i) becomes (3+1) + (4-2)i, which is 4 + 2i. Electrical engineers do this constantly when combining impedances in AC circuits, and physicists use it wherever waves and rotations are modeled. This calculator keeps the bookkeeping straight: enter the first number's pieces in Real Part 1 and Imaginary Part 1, the second number's in Real Part 2 and Imaginary Part 2, and read the Real Sum and Imaginary Sum results. Try the example above — 3, 4, 1, -2 — and confirm you get 4 and 2. No FOIL, no conjugates, no tricks; just two small additions wearing a fancy costume.

With the pre-filled defaults — Real Part 1 3, Imaginary Part 1 4, Real Part 2 1, Imaginary Part 2 -2 — the Adding Complex Numbers Calculator returns Real Sum 4.0000, Imaginary Sum 2.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.