Adding and subtracting complex numbers worksheets

Adding complex numbers is two sums side by side: the real parts, then the imaginary ones. These free printable worksheets stay on that first step, before multiplication and i² enter the picture.

Adding and subtracting complex numbers
Adding and subtracting complex numbers worksheet — Whole parts from −6 to 6, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

The idea to get across is that the two parts never mix. Three of i plus two of i is five of i, the way three apples and two apples are five apples, and that is all a student needs to stop trying to combine 3 and 2i. Subtracting asks one thing more, which is to take the minus through both parts of the second bracket.

Why this sheet works

Sometimes the imaginary parts cancel. (2 − 2i) + (4 + 2i) is 6, a plain real number, and a student can be thrown by an answer with no i in it. That result is correct and worth pointing out: real numbers are the complex numbers whose imaginary part is zero.

How this one works

(2 − 2i) + (4 + 2i)

2 + 4 = 6
−2 + 2 = 0
(2 − 2i) + (4 + 2i) = 6
  1. Add the two REAL parts, and leave the i alone. The real parts are 2 and 4.
  2. Now the two imaginary parts, the same way — this works because i is a number like any other here, so 2 of them plus 2 of them is what it sounds like.
  3. Put the two parts back together: 6.