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In a previous article, GFDVN was proposed, which is a convenient way of vector notation for geophysical fluid dynamics. This short note supplements the previous article of GFDVN with a systematic meth...od for the complex representation of two-dimensional real vectors. First, intimate relationships and correspondence rules are summarized between complex numbers and two-dimensional real vectors on plane. Most of useful GFDVN are expressed by arithmetic of complex numbers as well. Examples are presented to show that complex representation is often easier to handle with than GFDVN or traditional ones. In particular, strophe operator ¬, which rotates a vector clockwise at a right angle, is expressed simply as the multiplication of -i, the imaginary unit. Likewise two-dimensional Lagrange's formula for triple vector product is proved by a straightforward arithmetic way of complex numbers by virtue of correspondence rules. In addition, complex representation turns out to give a concise expression of vector operations and trigonometric identities.show more
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