Adding is just collecting like terms. Multiplying is FOIL with one extra rule. Dividing is the only one with a trick, and the trick is always the same: multiply by the conjugate of the bottom.
Leaving i² in the answer. It is -1, always, and forgetting that costs a sign on the real part. The other one is dividing without the conjugate: an i in the denominator means the answer is not finished.
Also called imaginary numbers, operations with i or arithmetic with complex numbers.
What you can put on this worksheet
Adding and subtracting
(4+i)−(−4−7i)→ 8+8i
Multiplying, where i² becomes -1
(3+i)(−3−5i)→ −4−18i
Dividing, using the conjugate
3+i−5−15i→ −3−4i
Questions about these worksheets
Yes. Every complex numbers sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the complex numbers questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 3: adding and subtracting, multiplying, where i² becomes -1 and dividing, using the conjugate. Tick as many as you want and set how many of each, or let it spread them evenly.
Leaving i² in the answer. It is -1, always, and forgetting that costs a sign on the real part. The other one is dividing without the conjugate: an i in the denominator means the answer is not finished.