Source: https://guthlabs.ai/docs/instruments/complex-number-calculator/
instrument / verified-clean
# Complex Number Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)
**Tranche**: tranche-4
**Evidence ID**: t4-141
**Ledger rows**: 1
No ledger note is attached.
## Review findings
The listed modulus, argument, and polar-multiplication formulas are standard under the stated assumptions, but the specification is incomplete for several claimed operations and leaves angle units, zero behavior, division-by-zero behavior, polar-radius constraints, normalization, and rounding ambiguous. The empty honest_label should be completed with these limitations and conventions.
### Formula and scope findings
- The supplied formulas for modulus and argument are correct: |z|=sqrt(a^2+b^2) and arg(z)=atan2(b,a), provided atan2 uses the stated angle unit.
- Polar multiplication is correctly described as multiplying moduli and adding arguments, but the angle unit and normalization range are unspecified.
- Formulas are missing for subtraction, rectangular multiplication, rectangular division, conjugation, and rectangular-to-polar inverse conversion, although the instrument claims to compute all of them.
- The argument of z=0 is undefined, so arg(0) cannot produce an ordinary numeric result.
- Polar form is non-unique unless a radius convention, normally r>=0, and an angle normalization range are specified.
### Unit assumptions
- All rectangular components a and b use the same unit, normally the underlying scalar numeric unit.
- Angles must explicitly be designated as radians or degrees; the test vectors use radians except where degrees are explicitly marked.
- atan2(b,a) returns an angle in the same unit requested for polar output.
- For polar input, r is assumed dimensionless or in the same scalar unit as the rectangular components, with r>=0 unless signed-radius behavior is explicitly supported.
## Boundary hardening
**BREAK_CLAIMED** · SELF_FLAGGED
The specification does not state whether polar angles are in degrees or radians, so an input such as 2∠90 has two valid but substantially different outputs. Zero has an undefined argument and zero-denominator division must also be rejected explicitly.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"inputs": {
"operation": "add",
"z1": "3+4i",
"z2": "1-2i"
},
"expected_outputs": {
"rectangular": "4+2i",
"modulus": 4.472135955,
"argument_radians": 0.463647609,
"polar": "4.472135955∠0.463647609 rad"
},
"working": "(3+4i)+(1-2i)=(3+1)+(4-2)i=4+2i. |z|=sqrt(4^2+2^2)=sqrt(16+4)=sqrt(20)=2sqrt(5)=4.472135955. arg(z)=atan2(2,4)=atan(1/2)=0.463647609 rad."
}
````
## Related workflows
No source-defined multi-instrument workflow membership is recorded.
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json · VERIFIED_CLEAN`
- `evidence-tranche4/tranche4-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`