A complex number has two parts and they never mix. These free printable worksheets add, subtract and multiply them, and work the powers of i, with every part a whole number and every answer written as a + bi.
Adding is two sums: the real parts, then the imaginary ones. It works because i behaves like any other symbol here — three of them plus two of them is five of them — and saying that out loud is what stops a student trying to combine 3 and 2i.
Why this sheet works
Multiplying is ordinary bracket expansion up to the last term, and then one thing happens that has no counterpart in anything before it: i² is not a symbol to carry, it is −1, and a term that looked imaginary turns real and joins the other side. Every answer key gives that step a line of its own, because every wrong answer on this skill is that step missed or its sign dropped.
How this one works
One question from this sheet, worked through a step at a time.
(3 − 5i) + (6 − 6i)
3 + 6 = 9
−5 + (−6) = −11
(3 − 5i) + (6 − 6i) = 9 − 11i
Add the two REAL parts, and leave the i alone. The real parts are 3 and 6.
Now the two imaginary parts, the same way — this works because i is a number like any other here, so 5 of them plus 6 of them is what it sounds like.
