AMC 12 Trigonometry & Complex Numbers Flashcards
6 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 6 AMC 12 Trigonometry & Complex Numbers flashcards as text
What is the product (2 + 3i)(2 − 3i)?
Answer: 13
(2 + 3i)(2 − 3i) = 4 − 9i² = 4 + 9 = 13.
In triangle ABC, angle A = 30°, b = 6, c = 4. What is the area of the triangle?
Answer: 6
Area = (1/2)bc·sin(A) = (1/2)(6)(4)(1/2) = 6.
What is tan(π/4)?
Answer: 1
tan(π/4) = sin(π/4)/cos(π/4) = (√2/2)/(√2/2) = 1.
What is the real part of (1 + 2i)/(1 − i)?
Answer: −1/2
Multiplying by the conjugate: (1+2i)(1+i)/2 = (−1+3i)/2, giving real part −1/2.
Which expression correctly states the sine angle-addition formula?
Answer: sin A·cos B + cos A·sin B
The angle-addition identity is sin(A + B) = sin A·cos B + cos A·sin B.
What is |e^(iπ) + 1|?
Answer: 0
By Euler's formula e^(iπ) = −1, so e^(iπ) + 1 = 0, and |0| = 0.
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