## Complex Numbers from A to ...Z* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory |

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ABCD angle Applying area[ABC assume called centroid circle circumcenter circumradius claimed collinear complex numbers complex plane Compute conclusion Consider Consider the complex coordinates of points Corollary denoted desired determined distance distinct equal equation equilateral triangle equivalent Figure Finally Find follows formula geometric images given gives hand hence holds identity ifand implies inequality last relation lengths Let Z1 lies mapping midpoint multiple Note Observe obtain oriented orthocenter points A1 polar polygon polynomial positive integer Problem Problem 13 Proof properties Proposition Prove quadrilateral real numbers real product regular relation Remark respectively result roots roots of unity rotation segment sides similar Solution square Subsection Suppose Theorem triangle A1A2A3 triangle ABC vertices write yields