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比较算法的重要指标。目前常用的基本符号包括大O、大Ω、大Θ、小o和小ω符号。这些符号均将时间视为实数实体，即时间与阿尔冈平面中的实轴重合。但若时间并非完全与阿尔冈平面实轴重合，而是与其成一定角度呢？我们试图聚焦于时间复杂度同时包含实部和虚部的情形。例如，若$T\left(n\right)=\ n\log{n}$，现有渐近符号能够实时处理该问题；但若遇到$T\left(n\right)=\ n\log{n}+i\cdot n^2$（其中$i=\sqrt[2]{-1}$）的情形，现有渐近符号将无法应对。为缓解此问题，本研究拟提出Zeta符号（$\zeta$），该符号能根据阿尔冈平面在实轴和虚轴上共同表征时间复杂度。