Q.49. Complexnumber, Polygon

Question 49.

Consider an n-sided regular polygon A1,A2......An having its centre at origin. If  Z1 represents the vertex A1,  then the complex number representing the vertex that is adjacent to A1 is___?

Answer 49.

Let r = radius of the circumscribing circle of the n-sided regular polygon.

Let Z1 = r (cosθ + isinθ) = r*e^(iθ)

Two adjacent vertices will have angular difference from θ of 2π/n
=> the adjacent vertices are
r*e^[i(θ ± 2π/n)]
= r*e^(iθ)*e^(±2π/n)
= Z1*e^(±2π/n).

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