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Complex Numbers |
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![]() Basic Definitions ![]() Algebraic Operations ![]() Complex Conjugation
![]() The Complex Plane ![]() Complex Numbers in Polar Coordinate System ![]() The Euler Formula Trigonometric Applications Algebraic Applications
![]() Complex Roots |
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Complex Roots
In view of periodicity of trigonometric functions sine and cosine, a complex number can be rewritten in the polar form as follows: The nth roots of z are determined by expression By substituting m = 0, 1, 2, 3, ... we obtain all roots tm of a complex number. There exist n different roots exactly: The next value of integer m gives the root tn+1 that coincides with t1: Note that all roots have the same modulus There is a simple way to plot all n
roots of a number z when one of the
roots is known. We need only to divide the circle with radius
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