hi there I have an assignment about lines and circles in the complex plane and there are some things I dont understand. I know that the equation of a line in terms of complex numbers can be written as AZ + AZ = c. and we get to know that A is perpendicular to the line AZ +AZ = c which i dont understand why. and then iA is parallell to the line. then its written that the nearest point to the origin on the line is cA 2jAj2 which i also dont understand how. then its written that the reection in the line is given by the map S(Z) = cA ?? A2Z how do they get to this equation? and how do i nd the formula for reection of a line for instance the line x + y = 1. and how do i nd the opposite how do i nd in which line for instanse S(Z) = Z ?? i is a reection? and about circles how do i nd the equation of a circle centre i and lets say radius 2? if i know that points on the circle centre C and radius r are given by the equation jZ ?? Cj = r or (Z ?? C)(Z ?? C) = r2 which when multiplied out becomes ZZ ?? CZ + CZ + CC = r2 And then if B lies on the circle centre C and radius r how do i show that the equation of the tangent at B is (B ?? C)Z + (B ?? C)Z = BB ?? CC + r2

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# hi there I have an assignment about lines and circles i

Tuesday July 12, 2022

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