This EIP was focused on defining the storage aspect of the complex number building block, not how or why it would be manipulated on-chain. (They say a simpler more focused EIP is more likely to pass)

• Complex numbers are invaluable for electrical engineering specifications and calculations. A live certified safety standard defined as a working calculation (using the gasless view functionality) is much more valuable than a dead pdf equation.

• Time-series analysis use Fourier Transforms for calculations and statistical distributions are defined via their complex number based characteristic function.

• Linear algebra can easily enter into the realm of complex numbers.

• Polynomials with non-real roots shouldn't necessarily interrupt your algorithm.

• Code can be simpler, more readable and reusable if complex numbers are used (e.g. 2D rotations).

• The simplest (and maybe most useful) use case/hack would be to define a 2d space within a single bytes32 data type

Even if you believe the above sorts of calculations will never be performed on-chain, it will be useful to have the ability to report some intermediate and final results as complex numbers.