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Let w⁴ = 16j. Which of the following cannot be a value of w?

1. 2e^(j2π/8)
2. 2e^(jπ/8)
3. 2e^(j5π/8)
4. 2e^(j9π/8)

Correct answer: 2e^(j2π/8)

Solution

16j = 16 e^{j pi/2}, so w = 2 e^{j(pi/8 + k pi/2)}: angles pi/8, 5pi/8, 9pi/8, 13pi/8. The angle 2pi/8 = pi/4 (option A) is not among them, so it cannot be a value. Stored answer (pi/8) is in fact a valid root, hence wrong; correct is 2e^{j2pi/8}.

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