Answer: 4cos³θ - 3cosθ.
- A 3cosθ - 4cos³θ
- B cos³θ - sin²θ
- C 3cos²θ - 1
- D 4cos³θ - 3cosθ
Correct answer: D. 4cos³θ - 3cosθ
Explanation: (cos theta + i sin theta)3 = cos 3theta + i sin 3theta. LHS expansion: real part = cos3theta - 3cos theta sin2theta = cos3theta - 3cos theta(1-cos2theta) = 4cos3theta - 3cos theta.
A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.
Concept context
Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots
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