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The knowledge of mutual impedance between buried conductors is of great importance in the field of electric energy systems, for studying power transmission and grounding systems behavior, especially during transient phenomena. In the present work we present novel expressions for calculating the mutual impedance between finite length conductors of arbitrary position in a homogeneous earth. The resulting expressions have the form of a double integral which we initially evaluate by adaptive quadratures. We then present a technique for alternatively calculating these expressions utilizing Sommerfeld integrals and the Discrete Complex Image Method.