This notation was more common in the post WWII era when typewriters were used to convey mathematical expressions.
Superscripts are both offset vertically and smaller than 'cis' or 'exp'; hence, they can be problematic even for hand writing. For example "e"<sup> "ix"²</sup> versus cis("x"²) versus exp("ix"²). For many readers, cis("x"²) is the clearest, easiest to read of the three.

The cis notation is sometimes used to emphasize one method of viewing and dealing with a problem over another. The mathematics of trigonometry and exponentials are related but not exactly the same; exponential notation emphasizes the whole, whereas cis and cos&nbsp;+&nbsp;"i"&nbsp;sin notations emphasize the parts. This can be rhetorically useful to mathematicians and engineers when discussing this function, and further serve as a mnemonic (for cos&nbsp;+&nbsp;"i"&nbsp;sin).

The cis notation is convenient for math students whose knowledge of trigonometry and complex numbers permit this notation, but whose conceptual understanding doesn't yet permit the notation "e"<sup> "ix"</sup>. As students learn concepts that build on prior knowledge, it is important not to force them into levels of math they are not yet prepared for.

मौलिक सम्बन्ध
The Gudermannian function
Convenience
ऐतिहासिक पृष्टभूमि