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Q.

Let 1a1−2i,1a2−2i,1a3−2i,1a4−2i,1a5−2i,1a6−2i,1a7−2i,1a8−2i  are vertices of regular octagon. If the area of octagon is A, then the value of 82A is (where aj∈R for j=1,2,3,4,5,6,7,8  and i=−1 ) _____

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answer is 2.

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Detailed Solution

x+iy=ar+2i(ar)2+4 ⇒x=arar2+4,y=2ar2+4x2+y2=12yx2+y2−12y=0So all points lie on circle x2+y2−y2=0and r=14∴Area of regular octagon = 8(12×r2×sin(2π8)) = 8×12×116×12=142
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Let 1a1−2i,1a2−2i,1a3−2i,1a4−2i,1a5−2i,1a6−2i,1a7−2i,1a8−2i  are vertices of regular octagon. If the area of octagon is A, then the value of 82A is (where aj∈R for j=1,2,3,4,5,6,7,8  and i=−1 ) _____