A complex structure gives rise to a conformal structure by choosing the standard Euclidean metric given on the complex plane and transporting it to X by means of the charts. Showing that a conformal structure determines a complex structure is more difficult.See for the construction of a corresponding complex structure.
a compleX stRuctuRe GiVes riSE tO a coNFOrmal stRuCture bY chOOsing thE StanDArd eucliDEan metric giVeN on the cOMpleX Plane And trAnSpOrtIng it TO X By Means of thE CharTs. shoWing thAt a CoNformal strucTure deTERMiNeS a compLeX strucTuRe iS more DiFFICULt.sEe fOR The COnstructIon Of a corREsPondinG complEX strUctuRE.