Locating Points in the Complex Plane (Quadrant/Axis)

The question asks to determine in which quadrant or on which axis a given complex number's corresponding point lies.

gaokao 2019 Q2 5 marks View
Let $z = - 3 + 2 i$. Then in the complex plane, the point corresponding to $\bar { z }$ is located in
A. the first quadrant
B. the second quadrant
C. the third quadrant
D. the fourth quadrant
gaokao 2021 Q1 View
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.
gaokao 2022 Q1 5 marks View
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
gaokao 2023 Q1 5 marks View
In the complex plane, the point corresponding to $(1+3i)(3-i)$ is located in
A. the first quadrant
B. the second quadrant
C. the third quadrant