In terms of verb/adjective conjugations, two common forms are ~아/어/여요 [which depends on the stem-end vowel] and ~ㅂ/습디다 (in present), and ~았/었/였 어요 and ~았/었/였 습디다 (in past).
For the verb 이기다, stem ends with vowel ㅣ(of 기), and thus the stem end is replaced by vowel ㅕ.
Hence, conjugations become,
Present
이겨요 and 이깁니다 ;
Past
이겼어요 and 이겼습니다 .
In the case of honorific, the basic form are replaced from 다 to 시다. The verb becomes 이기시다.
Conjugations of the two common forms become ~세요 and ~십니다 (in present), and ~셨어요 and ~셨습니다 (in past).
Hence, conjugations in honorific form become,
Present
이기세요 and 이기십니다 ;
Past
이기셨어요 and 이기셨습니다 .
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좋은 하루 :).