Question

Which expression represents a 5th root of –i?

Answer 1

Use DeMoivre's formula:

(cos(θ) + i sin(θ))ⁿ = cos(n θ) + i sin(n θ)

If a given number is a 5th root of -i, raising it to the 5th power should return -i.

Since -i = cos(-π/2) + i sin(-π/2), you should check any number with an argument θ such that 5θ = -π/2. This happens only for the last choice:

(cos(7π/10) + i sin(7π/10))⁵ = cos(35π/10) + i sin(35π/10)

and 35π/10 is equivalent to -π/2 (modulo 2π).

Answer 2

Answer: short answer D

Step-by-step explanation:

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