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Taking into account a relativistic multiplet structure of Ir ions, we have calculated the optical conductivity $\\sigma(\\omega)$ and resonant inelastic x-ray scattering (RIXS) spectra, which manifest different features from those of a canonical $j_{eff}$=$\\frac{1}{2}$ system Sr$_2$IrO$_4$.Distinctly from the two-peak structure in Sr$_2$IrO$_4$, $\\sigma(\\omega)$ in Na$_2$IrO$_3$ has a broad single peak dominated by interband transitions from $j_{eff}$=$\\frac{3}{2}$ to $\\frac{1}{2}$. 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