Answer: cos nθ + i sin nθ.
- A n cos θ + ni sin θ
- B cos θⁿ + i sin θⁿ
- C cos(θ/n) + i sin(θ/n)
- D cos nθ + i sin nθ
Correct answer: D. cos nθ + i sin nθ
Explanation: De Moivre theorem: (cos theta + i sin theta)<sup>n</sup> = cos(n*theta) + i sin(n*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
Read the full Complex Numbers and Quadratic Equations notes →