Complex Numbers
Complex Numbers
Allen Star Batch
Grade 11
Question:
If $|z| = 1$ and $z^{2n} + 1 + z^{-n} = 0$ then $\frac{z^{2n}}{2^{2n} + 1} - \frac{\left(\bar{z}\right)^n}{\left(\bar{z}\right)^{2n} + 1}$ is equal to ____.
Step-by-Step Solution
Key Concept: Evaluate the given expression by computing the series sum and taking absolute value.
Calculate $U_4 = \left|4\left(1 - \frac{1}{1!} - \frac{1}{2!} - \frac{1}{3!} - \frac{1}{4!}\right)\right| = 9$.
Correct Answer: 0