Imaginary numbers as part of complex numbers made their appearance in physical theories starting with Einstein’s theory of special relativity. Although complex analysis facilitates convenience in computational procedures for classical mechanics, electrodynamics, and thermodynamics, the implication is that the real parts are the ones that carry physical contents. There are three distinctive equivalent notations for a given complex number z: z = a + ib, z = r( cosq+ isinq), and z = rexp{iq}. The powers or products of z with itself indicate continuous conformal mapping of the complex plane into itself. Depending on the angular value of the rotational pivot vertex of a complex triangle, the continuous conformal mapping can produce self similarities with constant areas or progressively increasing or decreasing areas with clockwise or counterclockwise rotational invariance.


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