List of top Mathematics Questions on Algebra of Complex Numbers asked in KEAM

Let \( w \neq \pm 1 \) be a complex number. If \( |w| = 1 \) and \( z = \frac{w - 1}{w + 1} \), then \( \text{Re}(z) \) is equal to:

If \( z = e^{2\pi i / 3} \), then \( 1 + z + 3z^2 + 2z^3 + 2z^4 + 3z^5 \) is equal to:

The value of $\frac{1}{i}+\frac{1}{i^{2}}+\frac{1}{i^{3}}+\cdots+\frac{1}{i^{102}}$ is