Complex Number Addition Calculator

Work out complex number addition instantly with clear inputs, formula shown and shareable results.

About Complex Number Addition Calculator

Complex numbers add like two-dimensional vectors: real parts together and imaginary parts together. Geometrically that is the parallelogram rule in the Argand plane.

Formula

Complex addition

(a + bi) + (c + di) = (a + c) + (b + d)i

Worked example

With the default values below, Complex Number Addition Calculator returns Sum of 4 - 3i. Change any input above and every figure here is recalculated in your browser.

Inputs used

First real part: 3
First imaginary part: 4
Second real part: 1
Second imaginary part: -7

Results

Sum: 4 - 3i
Difference: 2 + 11i
Modulus of the sum: 5.00000000
Argument of the sum: -36.869898 °

Step by step

1Values used
2Complex addition
3Sum= 4 - 3i
4Difference= 2 + 11i
5Modulus of the sum= 5.00000000
6Argument of the sum= -36.869898 °

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Add 3 + 4i and 1 − 7i.

4 − 3i, of modulus 5 and argument −36.8698976°.

Why is addition so simple?

Because the real and imaginary axes are independent, exactly like the x and y components of a vector.