SAT Math: Operations with Complex Numbers
22+ practice questions in Praczo
The concept, explained
- 1
The imaginary unit i represents √−1, so i² = −1.
- 2
To add or subtract complex numbers, combine real parts with real parts and imaginary parts with imaginary parts: (a+bi) + (c+di) = (a+c) + (b+d)i.
- 3
To multiply, use FOIL and replace any i² with −1: (a+bi)(c+di) = ac + adi + bci + bdi² = (ac−bd) + (ad+bc)i.
- 4
To divide (or rationalize the denominator), multiply the numerator and denominator by the complex conjugate of the denominator: a−bi.
- 5
Powers of i loop every 4: i¹ = i, i² = −1, i³ = −i, i⁴ = 1.
- ✗ Forgetting to change i² to −1 when multiplying complex numbers, leaving the answer with an i² term.
- ✗ Adding real numbers directly to imaginary numbers (e.g., trying to say 3 + 4i is 7i).
SAT-style practice
What is the sum of (3 − 2i) and (4 + 6i)?
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