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...Introduction transformations lines unit circle more problems geometry in the complex plane hongyi chen uncawards banquet all is algebra many can be solved using a purely algebraic approach by placing geometric diagram on coordinate assigning each point an x y writing out equations of and circles solving these this method geo often called bashing quite powerful given right conditions but it has some issues with bash for are ugly two variables necessary random rotations extremely painful attempting to solve may result massive th degree polynomials fortunately xed replacing cartesian quick numbers acomplex number rectangular form bi where b real i wedene imaginary parts z as re im plotted placed horizontal axis vertical conjugate denoted its reection about any we have ab if only which occurs when similarly pure magnitude distance from origin then notice that zz between also expressed polar r cos sin angle formed positive ray starting at pointing towards measured counterclockwise simplicit...