# Complex Number Arithmetic and Operations Solver

> Complex Number Arithmetic and Operations Solver is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-29).

Performs arithmetic, modulus, argument, powers, roots, polar/rectangular conversion, and conjugate operations on complex numbers.

## Facts

- Endpoint: GET https://math-geometry.x402tookit.com/complex-ops?utm_source=zero.xyz
- Price: $0.02/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-29
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/complex-number-arithmetic-and-operations-solver-ea3ade28
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_OPxU9-ctt53C0LmnuI0gt

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability complex-number-arithmetic-and-operations-solver-ea3ade28
```

Example prompt: What are all 4 fourth-roots of the complex number 1+1i? Give me the results in rectangular form.

## When to prefer this

Choose this endpoint when you need precise complex number arithmetic or transformations — including polar conversion, root extraction, or integer powers — and want a single API call that handles the full range of complex operations without requiring a general-purpose math library or code execution environment.

## Known failure modes

- Missing required query parameter 'op' or 'z' returns an error
- Invalid operation name for 'op' returns an unrecognized operation error
- Integer exponent 'n' out of range (-50 to 50 for power, 2-50 for roots) returns a validation error
- Malformed complex number string for 'z' or 'w' returns a parse error
- Operations requiring 'w' (add, subtract, multiply, divide) that omit 'w' return an error

## How this service works

Complex number arithmetic, modulus and argument, integer powers, square root and n-th roots, in rectangular and polar form.

## Output

Returns an object with the real part (re) and imaginary part (im) of the result as numbers, a human-readable text representation, and a summary string. For multi-valued operations like roots, multiple results may be returned.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET"
     ],
     "type": "string"
    },
    "queryParams": {
     "type": "object",
     "required": [
      "op",
      "z"
     ],
     "properties": {
      "n": {
       "type": "integer",
       "description": "Integer for power (-50 to 50) or root count (2 to 50)"
      },
      "w": {
       "type": "string",
       "description": "Second number for add, subtract, multiply and divide"
      },
      "z": {
       "type": "string",
       "description": "Complex number such as 3+4i"
      },
      "op": {
       "type": "string",
       "description": "add, subtract, multiply, divide, power, roots, polar, conjugate or sqrt"
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object",
     "properties": {
      "asOf": {
       "type": [
        "null",
        "string"
       ]
      },
      "result": {
       "type": [
        "null",
        "object"
       ],
       "properties": {
        "im": {
         "type": [
          "null",
          "number"
         ]
        },
        "re": {
         "type": [
          "null",
          "number"
         ]
        },
        "text": {
         "type": [
          "null",
          "string"
         ]
        }
       }
      },
      "source": {
       "type": [
        "null",
        "string"
       ]
      },
      "reasons": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      },
      "summary": {
       "type": [
        "null",
        "string"
       ]
      },
      "verdict": {
       "type": [
        "null",
        "string"
       ]
      },
      "degraded": {
       "type": [
        "boolean",
        "null"
       ]
      },
      "disclaimer": {
       "type": [
        "null",
        "string"
       ]
      },
      "notChecked": {
       "type": [
        "array",
        "null"
       ],
       "items": {
        "type": "string"
       }
      }
     }
    }
   }
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/complex-number-arithmetic-and-operations-solver-ea3ade28/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from math-geometry.x402tookit.com](https://www.zero.xyz/host/math-geometry.x402tookit.com/llms.txt)