SAT Math · Additional Topics in Math
Complex numbers
Adding, subtracting, multiplying complex numbers.
What's tested in this subtopic
A small number of items test complex-number arithmetic. The key fact is i² = −1; multiplication is just FOIL with that substitution. Division by a complex number requires multiplying by the conjugate.
Tactics that actually move your score
When multiplying (a + bi)(c + di), FOIL and use i² = −1. When asked for a complex number in the form a + bi, group real and imaginary parts at the end. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy If 4x + 8 = 0, what is the value of x?
- Easy If 2x − 8 = 10, what is the value of x?
- Medium If 2x + 12 = 18, what is the value of x?
- Medium If 2x + 3 = 17, what is the value of x?
- Medium If 2x − 4 = 4, what is the value of x?
- Hard If 7x + 1 = 57, what is the value of x?
- Easy If 3x − 12 = 9, what is the value of x?
- Easy If 8x + 1 = 81, what is the value of x?
- Medium If 7x + 2 = 44, what is the value of x?
- Medium If 9x − 7 = -88, what is the value of x?
- Medium If 3x + 1 = -2, what is the value of x?
- Hard If 2x + 3 = -17, what is the value of x?
- Easy If 9x − 7 = 74, what is the value of x?
- Easy If 3x − 11 = -23, what is the value of x?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.