An answer is not finished while an i sits on the bottom. Multiplying top and bottom by the conjugate of the denominator clears it, because a number times its conjugate is always real.
Select your difficulty
Pick more than one for a sheet that mixes them.
The preview can look cramped on a phone. The PDF and printed sheet come out normal.
Changing the sign on the wrong part. The conjugate flips the sign of the imaginary part only: the conjugate of 3 + i is 3 - i, not -3 + i.
Also called complex conjugate or rationalizing complex denominators.
What you can put on this worksheet
Dividing, using the conjugate
3+i−5−15i→ −3−4i
Answers with fractions
1−3i6→ 53+59i
Questions about these worksheets
Yes. Every dividing 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 dividing 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 2: dividing, using the conjugate and answers with fractions. Tick as many as you want and set how many of each, or let it spread them evenly.
Changing the sign on the wrong part. The conjugate flips the sign of the imaginary part only: the conjugate of 3 + i is 3 - i, not -3 + i.