If $Z_n=\operatorname{cis}\left(\frac{\pi}{n(n+1)(n+2)}\right)$ for $n=1,2,3 \ldots$. and $Z = \mathop {\lim }\limits_{n \to \infty } \left( {{z_1}{z_2} \ldots .{z_n}} \right)$, then principal argument of $Z$ is

JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Z_n=\operatorname{cis}\left(\frac{\pi}{n(n+1)(n+2)}\right)

for

n=1,2,3 \ldots

. and

Z = \lim\limits_{n \to \infty } \left( {{z_1}{z_2} \ldots .{z_n}} \right)

, then principal argument of

Z

View answer and explanation

Correct option: C

\frac{\pi}{4}

Option C (

\frac{\pi}{4}

) is correct because the principal argument of the limit of the product of complex numbers

Z_n

\frac{\pi}{4}

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