can the past tense of 来る be written in kanji？


can きた be written in kanji like this 来た?




Yes, the result would be 来た。 The same can be said of other kanji as well,
hiragana was in part developed so that you can conjugate verbs and still use
the kanji.

to come 来る can be conjugated using the kanji as follows:

> 来｛く｝る
>
> 来｛き｝た
>
> 来｛こ｝ない
>
> 来｛こ｝なかった
>
> 来｛こ｝い (imperative command--very direct)

another example: to run (走る）

> そこへ走る。
>
> そこへ走った。
>
> そこへ走らない。
>
> そこへ走らなかった。

As you can see, the hiragana is where the conjugation magic happens, and the
kanji is left untouched. If you're ever in doubt, you can at least be safe in
assuming that you would use the kanji regardless.

