A computer-based information system is a system that utilizes computer technology to transform raw data into meaningful information. It involves the use of hardware, software, data, and people to collect, process, store, and distribute information for decision-making and problem-solving purposes.

Here is a detailed explanation of each option and why option 'A' is the best choice:

a) A system in which a computer is used to turn data into information:
This option accurately describes a computer-based information system. Computers are used to process and analyze raw data, converting it into useful information that can be used for various purposes. The computer performs operations such as sorting, filtering, organizing, and summarizing the data to generate meaningful outputs.

b) Inputting data:
While inputting data is an important aspect of a computer-based information system, it is not the complete definition. Inputting data involves entering raw data into the computer system, but this data needs to be processed and analyzed to derive useful information.

c) Processing data:
Processing data is another crucial component of a computer-based information system. Once the data is inputted, it undergoes various processing operations to convert it into meaningful information. This includes tasks such as calculations, comparisons, data transformations, and data manipulations.

d) Performing complex mathematical calculations:
While computer-based information systems can perform complex mathematical calculations, this option does not encompass the full scope of such systems. Computer-based information systems go beyond just calculations and involve the entire process of collecting, storing, processing, and distributing information.

In conclusion, option 'A' is the best choice as it accurately captures the essence of a computer-based information system, which is the utilization of computers to convert raw data into meaningful information.