Represent a complex number a+b*i by the ordered integer pair [a,b], with i²=−1. Keep the real component first and the imaginary coefficient second; graph appearance supplies no missing values. No complex division or polar form is used here. value=[5, 0], real candidate=5. Give (value,real candidate,is the imaginary coefficient zero?,is value exactly [candidate,0]?).
G001 — Represent a complex number a+b*i by the ordered integer pair [a,b], with i²=−1. Keep the real component first and the imaginary coefficient second; graph appearance supplies no missing values. No complex division or polar form is used here. value=[5, 0], real candidate=5. Give (value,real candidate,is the imaginary coefficient zero?,is value exactly [candidate,0]?).
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Use this bank exact ordered tuple and hyphenated operation.Rational outputs reduce with positive denominators and OMIT/1 for integers,unlike the preceding legacy bank.Do not change original bilingual snapshots or meaning.
a+bi is in the real embedding IFF b=0.Matching THIS candidate also requires a=candidate.The first flag may be True while matching is False;the candidate bound is±1e6,not the pair component bound1000.
S002 · premise_and_result_audit — Reverse-check every ORIGINAL coordinate/table entry/alignment and strict premise,not just the final answer.Keep finite candidates,general reasoning,formal proof and publication responsibilities distinct.
S001 · premise_and_result_audit — Reverse-check every ORIGINAL coordinate/table entry/alignment and strict premise,not just the final answer.Keep finite candidates,general reasoning,formal proof and publication responsibilities distinct.
Result
([5, 0], 5, Yes, Yes)
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.