JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

Two conjugate complex numbers

z_1

and

\overline{z_1}

represent two adjacent vertices of a polygon of

\mathrm{n}

sides, whose centre is origin. If

\frac{\operatorname{Im}\left(z_1\right)}{\operatorname{Re}\left(\bar{z}_1\right)}=\sqrt{2}-1

then ratio of the areas of the circles inscribed and circumscribed the polygon is

View answer and explanation

Correct option: C

\frac{\sqrt{2}+1}{2 \sqrt{2}}

Option C (

\frac{\sqrt{2}+1}{2 \sqrt{2}}

) is correct because it represents the square of the cosine of

\frac{\pi}{8}

, which is the ratio of the inscribed to circumscribed circle areas.

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