1. The point corresponding to the complex number $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } }$ in the complex plane is located in which quadrant? A. First quadrant B. Second quadrant C. Third quadrant D. Fourth quadrant 【Answer】A 【Solution】 【Analysis】Use complex division to simplify $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } }$, and thus determine the location of the corresponding point. 【Detailed Solution】 $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } } = \frac { ( 2 - \mathrm { i } ) ( 1 + 3 \mathrm { i } ) } { 10 } = \frac { 5 + 5 \mathrm { i } } { 10 } = \frac { 1 + \mathrm { i } } { 2 }$, so the point corresponding to this complex number is $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$, which is located in the first quadrant. Therefore, the answer is: A.
1. The point corresponding to the complex number $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } }$ in the complex plane is located in which quadrant?\\
A. First quadrant\\
B. Second quadrant\\
C. Third quadrant\\
D. Fourth quadrant\\
【Answer】A\\
【Solution】\\
【Analysis】Use complex division to simplify $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } }$, and thus determine the location of the corresponding point.\\
【Detailed Solution】 $\frac { 2 - \mathrm { i } } { 1 - 3 \mathrm { i } } = \frac { ( 2 - \mathrm { i } ) ( 1 + 3 \mathrm { i } ) } { 10 } = \frac { 5 + 5 \mathrm { i } } { 10 } = \frac { 1 + \mathrm { i } } { 2 }$, so the point corresponding to this complex number is $\left( \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$, \\
which is located in the first quadrant. \\
Therefore, the answer is: A.\\