Suppose \({x_1}\left( t \right)\) and \({x_2}\left( t \right)\) have the Fourier transforms as shown below.Which one of the following statements is TRUE?

• A. \({x_1}\left( t \right)\) and \({x_2}\left( t \right)\) are complex and \({x_1}\left( t \right){x_2}\left( t \right)\) is also complex with nonzero imaginary part
• B. \({x_1}\left( t \right)\) and \({x_2}\left( t \right)\) are real and \({x_1}\left( t \right){x_2}\left( t \right)\) is also real
• C. ​\({x_1}\left( t \right)\) and \({x_2}\left( t \right)\) are complex but \({x_1}\left( t \right){x_2}\left( t \right)\) is real
• D. \({x_1}\left( t \right)\) and \({x_2}\left( t \right)\) are imaginary but \({x_1}\left( t \right){x_2}\left( t \right)\) is real