Answer: 0.
- A 1
- B 5
- C z⁵
- D 0
Correct answer: D. 0
Explanation: z=e<sup>2πi/5</sup> is a primitive 5th root of unity, so z⁵=1. The sum 1+z+z²+z³+z⁴ is a geometric series: (z⁵-1)/(z-1)=(1-1)/(z-1)=0. Alternatively, it equals the sum of ALL 5th roots of unity, which always equals 0. Answer: sum = 0
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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