$z=1-\frac{i}{1-\frac{1}{1+i}}$ জটিল সংখ্যাটির মডুলাস ও আর্গুমেন্ট-

$1,\frac{3 \pi}{2}$ Explanation: $z = \frac{1 - i}{1 + i} = \frac{1 - i}{1 + i} \cdot \frac{1 - i}{1 - i} = \frac{(1 - i)^2}{(1 + i)(1 - i)} = \frac{1 - 2i + i^2}{1 - i^2} = \frac{1 - 2i - 1}{1 - (-1)} = \frac{-2i}{2} = -i$ $|z| = |-i| = 1$ $\arg(z) = -\frac{\pi}{2} \; \text{or} \; \frac{3\pi}{2}$ $\boxed{|z| = 1, \; \arg(z) = \tfrac{3\pi}{2}}$ N.B: - $\frac{\pi}{2} \; \text{and} \; \frac{3\pi}{2}$ are same