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NDA (II) 2022 · Mathematics

A full Mathematics paper in the UPSC NDA pattern. 120 questions in 150 minutes, with a third of the marks deducted for every wrong answer.

120questions

300marks

+2.5 / −0.83per question

43/64/13easy / medium / hard

Sections and topics

One 120-question Mathematics paper covering algebra, trigonometry, calculus, geometry, vectors, statistics and probability.

Complex numbers · medium

For every positive integer

n

, the value of

\left(\dfrac{1+i}{1-i}\right)^{4n+3}

Show answer and solution

Answer: C

\frac{1+i}{1-i}=\frac{(1+i)^2}{2}=\frac{2i}{2}=i

. So the expression is

i^{4n+3}=i^3=-i

. Powers of

i

repeat with period

4