Time Complexity is an important metric to compare algorithms based on their cardinality. The commonly used, trivial notations to qualify the same are the Big-Oh, Big-Omega, Big-Theta, Small-Oh, and Small-Omega Notations. All of them, consider time a part of the real entity, i.e., Time coincides with the horizontal axis in the argand plane. But what if the Time rather than completely coinciding with the real axis of the argand plane, makes some angle with it? We are trying to focus on the case when the Time Complexity will have both real and imaginary components. For Instance, if $T\left(n\right)=\ n\log{n}$, the existing asymptomatic notations are capable of handling that in real time But, if we come across a problem where, $T\left(n\right)=\ n\log{n}+i\cdot n^2$, where, $i=\sqrt[2]{-1}$, the existing asymptomatic notations will not be able to catch up. To mitigate the same, in this research, we would consider proposing the Zeta Notation ($\zeta$), which would qualify Time in both the Real and Imaginary Axis, as per the Argand Plane.

翻译：时间复杂度是基于算法基数进行比较的重要指标。常用的简单符号包括大O、大Ω、大Θ、小o和小ω符号。所有这些符号均将时间视为实数实体的一部分，即时间与阿尔冈平面中的水平轴重合。然而，若时间并非完全与阿尔冈平面的实轴重合，而是与之形成一定夹角，又当如何？我们致力于聚焦于时间复杂度同时具有实部和虚部的情形。例如，若 $T(n)=n\log{n}$，现有渐近符号可实时处理；但若遇 $T(n)=n\log{n}+i\cdot n^2$（其中 $i=\sqrt[2]{-1}$），现有渐近符号则无法应对。为解决此问题，本研究拟提出泽塔符号（$\zeta$），该符号将依据阿尔冈平面，同时量化时间在实轴和虚轴上的特性。