Understanding Complex Valued Magnetic Fields

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chrisjk
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I have a complex valued (magnetic) vector field. In order to find the actual magnitude, do I need to multiply by the complex conjugate? If I remember correctly, the direction is given only by the real part. Can anyone verify this?
 
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The real part might be the total field, and the imaginary part could be just a calculation artifact. But that really depends on the way that complex field is constructed.

Direction in the real part and magnitude in the magnitude of the complex vector looks strange to me (but this does not mean it is impossible).