wiem ty chcialbym: is this correct spelling

is this how you would write in poliash -i know you want to

wiem ty chcialbym-

wiem, że chcesz

do you use chcialbym when reffering to I or does it mean something else?

Ja chciałbym.... = I would like to...

and
I know (that) you would like to ... - Wiem, że chciałbyś / chciałabyś ... [talking to a male / female]

a quick overview of conditional forms
I / you / he would like to ... - chciałbym / chciałbyś / chciałby
we / you / they would like to ... - chcielibyśmy / chcielibyście / chcieliby
(when the subject is female, you change "chciał" to "chciała", "chcieli" to "chciały" and the -by endings behave still like for masculine gender: for example she would like to ... - chciałaby)

Ja wiem, że ty chciałbyś
Ja wiem, że ty chciałabyś

I would have thought that depending on the sex of the second person both sentences were possible.