Additional Topics in Math

Complex Numbers

Add, multiply, and simplify complex number expressions. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on complex numbers is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 What is the product (-6 + 5i)(3 + 5i) expressed in the form a + bi? easy 400-500 Open
2 What is the product (4 - 4i)(1 + 4i) expressed in the form a + bi? easy 400-500 Open
3 What is the product (-2 - 1i)(2 + 1i) expressed in the form a + bi? easy 400-500 Open
4 What is the product (6 + 6i)(-6 - 2i) expressed in the form a + bi? easy 400-500 Open
5 What is the product (-6 + 4i)(-1 - 1i) expressed in the form a + bi? easy 400-500 Open
6 What is the product (-2 + 6i)(-4 - 4i) expressed in the form a + bi? easy 400-500 Open
7 What is the product (1 - 2i)(4 - 1i) expressed in the form a + bi? easy 500-600 Open
8 What is the product (-2 + 2i)(6 + 4i) expressed in the form a + bi? easy 500-600 Open
9 What is the product (4 + 6i)(-2 - 2i) expressed in the form a + bi? medium 500-600 Open
10 What is the product (6 + 2i)(4 - 5i) expressed in the form a + bi? medium 500-600 Open
11 What is the product (-1 + 4i)(-5 + 2i) expressed in the form a + bi? medium 500-600 Open
12 What is the product (1 - 2i)(-2 + 4i) expressed in the form a + bi? medium 500-600 Open
13 What is the product (-6 - 2i)(-1 + 6i) expressed in the form a + bi? medium 600-700 Open
14 What is the product (1 - 4i)(-4 + 1i) expressed in the form a + bi? medium 600-700 Open
15 What is the product (1 - 6i)(-1 + 6i) expressed in the form a + bi? medium 600-700 Open
16 What is the product (4 + 6i)(5 + 4i) expressed in the form a + bi? medium 600-700 Open
17 What is the product (2 - 1i)(1 + 5i) expressed in the form a + bi? medium 600-700 Open
18 What is the product (-1 + 6i)(2 + 3i) expressed in the form a + bi? medium 600-700 Open
19 What is the product (1 - 1i)(-2 + 1i) expressed in the form a + bi? hard 600-700 Open
20 What is the product (4 - 1i)(4 + 5i) expressed in the form a + bi? hard 700-800 Open
21 What is the product (-1 - 1i)(-3 - 1i) expressed in the form a + bi? hard 700-800 Open
22 What is the product (1 - 5i)(5 - 4i) expressed in the form a + bi? hard 700-800 Open
23 What is the product (-2 - 6i)(-6 + 1i) expressed in the form a + bi? hard 700-800 Open
24 What is the product (5 - 2i)(-3 + 4i) expressed in the form a + bi? hard 700-800 Open
25 What is the product (1 - 5i)(1 - 1i) expressed in the form a + bi? hard 700-800 Open