Question Detail
Question
Express \(e^{(1 - \frac{\pi}{4}i)}\) as a product
Correct Answer
Option B is the correct answer.
Detailed Explanation
(e^{1 - i\pi/4} = e \cdot e^{-i\pi/4} = e(\cos(\pi/4) - i\sin(\pi/4)) = e\left(\frac{\sqrt{2}}{2} - i\frac{\sqrt{2}}{2}\right) = \frac{e}{\sqrt{2}}(1 - i)).
Hint
Use Euler's formula: \(e^{i\theta} = \cos\theta + i\sin\theta\).