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The one loop supersymmetric electro-weak correction to the anomalous magneticmoment of the muon is derived in the minimal N=1 supergravity unification withtwo CP violating phases. A numerical analysis of the CP violating effects on$g_{\mu}-2$ is carried out with the cancellation mechanism to guarantee thesatisfaction of the experimental limits on the electric dipole moments of theelectron and on the neutron. It is found that the effects of the CP phases cansignificantly affect the supersymmetric electro-weak correction to $g_{\mu}-2$,and that the numerical size of such a correction can be as large or larger thanthe Standard Model electro-weak correction to $g_{\mu}-2$. These results are ofimport for the new Brookhaven experiment which is expected to increase thesensitivity of the $g_{\mu}-2$ measurements by a factor of 20 and allow for atest of the electro-weak correction in the near future.Comment: Minor changes in text. This version to appear in Physical Review D.  19 pages, 4 fig

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation and the muon anomaly in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:math>supergravity

CPviolation and the muon anomaly inN=1supergravity