Read the result
Addition and subtraction move components directly. Multiplication combines scaling and rotation, so the result is often easier to understand on the Argand plane.
Complex numbers
Complex Number Calculator
Work through complex arithmetic while keeping rectangular and polar meaning visible.
Formula
(a+bi)(c+di) = (ac - bd) + (ad + bc)i
Result
Worked substitution
Rectangular form is convenient for addition; polar thinking is often clearer for multiplication.
Where it helps
Good for checking hand calculations before using complex numbers in loci, roots, or AC circuit work.
Common slip
For division, the denominator is c^2 + d^2. If c and d are both zero, the operation is not defined.
Try it
Multiply i by i using z1 = 0 + 1i and z2 = 0 + 1i. The result should explain why i^2 = -1.