Norm of bounded operator on a complex Hilbert space.

It is fairly easy to show that for a bounded linear operator $T$ on a Hilbert space $H$$$\|T\|=\sup_{\|x\|=1,\|y\|=1}|\langle y, Tx \rangle |.$$If $H$ is a complex Hilbert space, can you show that$$\|T\|=\sup_{\|x\|=1}|\langle x, Tx \rangle |\;?$$