Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

No annotations are provided, so the description carries the full burden. It does add genuinely useful behavioral context that the schema cannot express: the internal use of hypot and the paid/trial model ('5 free trial calls per signed wallet'), which tells the agent there is a wallet-signed metering/auth dimension. It does not disclose error behavior, whether params are optional, or what happens when both alias forms are supplied.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

The functional sentence is front-loaded and compact, and the parameter aliasing hint is attached directly to the operation it affects. The trailing emoji marketing line is extraneous to tool selection but short enough not to obscure the core content.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple scalar math tool with no output schema and no annotations, the description covers the core operation adequately and hints at the pricing/auth model. The remaining gap is the ambiguity of four optional string parameters with no documented types or requiredness, which the description only partially resolves via the a/real and b/imag aliasing.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0% across 4 parameters, so the description must compensate. The phrase 'from real/a and imag/b' usefully signals that 'real' and 'a' (and 'imag' and 'b') are alternate spellings for the same value, which is not derivable from the schema. However, it leaves unresolved whether both forms may be passed together, which form takes precedence, and why 0 parameters are required.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Computes the magnitude of a complex number') and even names the underlying method (hypot), which distinguishes it from the sibling complex-* family (complex-add, complex-angle, complex-conjugate, etc.). It does not name those siblings explicitly, so routing relies on the reader inferring 'magnitude' is distinct from angle/conjugate.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

There is no statement of when to use this tool versus the other complex-number siblings, and no prerequisite or exclusion information. The only contextual cue is the pricing line about free trial calls, which says nothing about tool selection.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.