Which graph represents 2 times open paren cosine of open paren 2 pi over 3 close paren plus i sine open paren 2 pi over 3 close paren close paren ?
Answer
A
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (1, 1.75).
B
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (negative 1, 1.75).
C
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (negative 0.5, 1).
D
Image with description On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A point is around (0.5, 1).
Explanation
Use cos(2π/3) = −1/2 and sin(2π/3) = √3/2. Multiplying both parts by 2 gives −1 + i√3, which is the point (−1, √3), approximately (−1, 1.75). That matches choice C.
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