Answer:
Step-by-step explanation:
If in doubt, multiply them out.
(-i)^4 = i^4 = 1 . . . . . results for ±i
(-1)^4 = 1^4 = 1 . . . . . results for ±1
An even power of a negative number is equivalent to the same power of the opposite (positive) number. The even number of minus signs cancel in the final product.
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In trig form, unity is 1∠(n·360°) . . . . . for n = any integer
Then the 4th root is ...
1^(1/4) ∠(n·360°/4) = 1 ∠(n·90°) . . . . for n = 0...3 (angles repeat after that)
That is, the roots are ...
- 1∠0° = 1
- 1∠90° = i
- 1∠180° = -1
- 1∠270° = -i
Of these, all but the first are listed among your answer choices. The appropriate selection is <em>all of the above</em>. (recognizing that not all of the appropriate choices are "above" that answer selection).