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In this video tutorial on complex variables, branch points, and branch cuts are defined. The foundation for performing complex integration of functions with branches is discussed starting with the natural log of a complex number Z. The function W equals F of Z equals lon of Z is explored using the real and imaginary parts of a complex number as well as polar representation. The natural log of Z is expressed as the natural log of R plus I times theta where R and theta are positive real numbers in the complex plane.