{
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  "$id": "https://www.calculatorx.com/schemas/math.complex/1.3.0/input.json",
  "title": "Complex numbers — input",
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  "additionalProperties": false,
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      "maxLength": 80,
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      ],
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      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024
    },
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      "type": [
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      "maxLength": 1024
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      "type": [
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      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
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      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024
    },
    "arg_deg": {
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        "number",
        "string"
      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024,
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      ],
      "x-uuce-unit": {
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        "quantity_kind": "plane_angle",
        "dimension": [
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          0,
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          0,
          0,
          0
        ],
        "registry_version": "0.3.0-preview.3",
        "digest_contract": "calculatorx-unit-definition-digests-v2",
        "registry_status": "preview",
        "definition_lifecycle": "candidate",
        "role": "scalar"
      }
    },
    "n": {
      "type": [
        "number",
        "string"
      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024
    },
    "from": {
      "type": "string",
      "pattern": "^\\s*(?:[rR][eE][cC][tT]|[pP][oO][lL][aA][rR])\\s*$"
    },
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        "number",
        "string"
      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024
    },
    "im1": {
      "type": [
        "number",
        "string"
      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024
    },
    "arg": {
      "type": [
        "number",
        "string"
      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024,
      "x-unit": "deg",
      "x-unit-id": "cx:deg",
      "x-quantity-kind": "plane_angle",
      "x-role": "scalar",
      "x-dimension": [
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      ],
      "x-uuce-unit": {
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        "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
        "dependency_digest": "eef386126ec6524884c84bab06f2a96996df913376c0ce5ccdaca0e7faf7b9c3",
        "quantity_kind": "plane_angle",
        "dimension": [
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        ],
        "registry_version": "0.3.0-preview.3",
        "digest_contract": "calculatorx-unit-definition-digests-v2",
        "registry_status": "preview",
        "definition_lifecycle": "candidate",
        "role": "scalar"
      }
    },
    "exponent": {
      "type": [
        "number",
        "string"
      ],
      "pattern": "^[+\\-−–—]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+\\-]?\\d+)?$",
      "maxLength": 1024
    }
  },
  "allOf": [
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      "if": {
        "properties": {
          "mode": {
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        }
      },
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          "im2"
        ]
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    },
    {
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        "anyOf": [
          {
            "required": [
              "n"
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          },
          {
            "required": [
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          }
        ]
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    },
    {
      "if": {
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        },
        "required": [
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        ]
      },
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        "required": [
          "r"
        ],
        "anyOf": [
          {
            "required": [
              "arg_deg"
            ]
          },
          {
            "required": [
              "arg"
            ]
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  ],
  "description": "Rectangular and polar complex arithmetic, integer powers, nth roots, and Euler form. Not a CAS. (calculation_version 1.3.0)",
  "x-unit-contract": {
    "protocol": "calculatorx-field-unit-contract-v1",
    "capability_id": "math.complex",
    "registry_version": "0.3.0-preview.3",
    "declaration_scope": "Field/branch declarations only; inactive fields are not asserted to exist. No conversion-engine migration or new numerical certification.",
    "path_format": "Paths relative to inputs or result_detail.value; dot separates properties, * denotes array items, $ denotes a scalar result.",
    "inputs": {
      "arg_deg": {
        "unit": "deg",
        "reference": {
          "unit_id": "cx:deg",
          "revision": "1.0.0",
          "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
          "dependency_digest": "eef386126ec6524884c84bab06f2a96996df913376c0ce5ccdaca0e7faf7b9c3",
          "quantity_kind": "plane_angle",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "arg": {
        "unit": "deg",
        "reference": {
          "unit_id": "cx:deg",
          "revision": "1.0.0",
          "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
          "dependency_digest": "eef386126ec6524884c84bab06f2a96996df913376c0ce5ccdaca0e7faf7b9c3",
          "quantity_kind": "plane_angle",
          "dimension": [
            0,
            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      }
    },
    "outputs": {
      "arg_deg": {
        "unit": "deg",
        "reference": {
          "unit_id": "cx:deg",
          "revision": "1.0.0",
          "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
          "dependency_digest": "eef386126ec6524884c84bab06f2a96996df913376c0ce5ccdaca0e7faf7b9c3",
          "quantity_kind": "plane_angle",
          "dimension": [
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            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      },
      "roots.*.arg_deg": {
        "unit": "deg",
        "reference": {
          "unit_id": "cx:deg",
          "revision": "1.0.0",
          "content_digest": "ebb31e3abee53f3bf57339c87949e1018d141739fba8a07f54c42ebfd219262b",
          "dependency_digest": "eef386126ec6524884c84bab06f2a96996df913376c0ce5ccdaca0e7faf7b9c3",
          "quantity_kind": "plane_angle",
          "dimension": [
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            0,
            0,
            0,
            0,
            0,
            0
          ],
          "registry_version": "0.3.0-preview.3",
          "digest_contract": "calculatorx-unit-definition-digests-v2",
          "registry_status": "preview",
          "definition_lifecycle": "candidate",
          "role": "scalar"
        }
      }
    },
    "applicability": "Angular fields apply only when present in the selected complex operation; formatted euler/cis strings are not measured fields."
  }
}