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If `z_1 and bar z_1` represent adjacent vertices of a regular polygon of n sides where centre is origin and if `(Im(z))/(Re(z)) = sqrt(2) - 1`, then n is equal to: (A) 8 (B) 16 (C) 24 (D) 32 |
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Answer» Please refer to the diagram in the video. From the diagram, `tan theta = y/x` `tan theta = sqrt2-1` Now, `(2pi)/n = 2theta` `=>tan((2pi)/n) = tan2theta` `=>tan((2pi)/n) = (2tantheta)/(1-tan^2theta)` `=>tan((2pi)/n) = (2(sqrt2-1))/(1-(sqrt2-1)^2)` `=>tan((2pi)/n) = (2(sqrt2-1))/(1-(2+1-2sqrt2))` `=>tan((2pi)/n) = (2(sqrt2-1))/(2(sqrt2-1))` `=>tan((2pi)/n) = 1 = tan(pi/4)` `=>(2pi)/n = pi/4` `=> n = 8` So, option `A` is the correct option. |
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