DOI: 10.1109/itcs.2009.258
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Wang Rui, Yu Xuegang

Abstract: Hyperbolic imaginary unit and elliptic imaginary unit have corresponding complex spaces respectively. By utilizing Gudermannian function, the geometric relationships of two kinds of functions of a complex variable and complex planes can be established. The geometric connections of hyperbolic function and trigonometric function can be founded in the complex plane as well.