Solve a problem involving complex numbers

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The discussion revolves around solving a problem involving complex numbers, specifically analyzing a circle in the Argand plane with center at (√3, -1) and radius 1. Participants calculate the distance from the origin to the circle's center and derive the minimum distance to the origin, concluding it to be 1. They also explore the maximum argument of a point on the circle, with calculations leading to an angle of 60 degrees for the maximum argument. The conversation emphasizes the geometric relationships and analytical methods to solve the problem, including the use of derivatives and tangent lines.
  • #31
It is all about a ## 30^\circ-60^\circ-90^\circ ## triangle whose three angles are in the ratio ## 1:2:3 ## and whose three sides are in the ratio ## 1:\sqrt 3:2 ##. This triangle and its reflection over the hypotenuse form a right kite with two other angles of ## 60^\circ ## and ## 120^\circ ##.
 

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