Question

In the complex plane, the number $4 + 3i$ is located in the
A) First quadrant
B) Second quadrant
C) Third quadrant
D) Fourth quadrant

Answer 1

Notice the sign of the real and the complex part of the complex number to think about the quadrant. It is the same as any ordered pair on the plain. Real part of the given complex number is $4$ and the imaginary part of the complex number is $3$.

Complete step-by-step answer:
We have given a complex number $4 + 3i$.
The goal is to find the location of this given complex number.
Any complex number id formed by a real number and an imaginary number and this number can be expressed as:
$C = a + ib$, here $a$ is the real part of the complex number and $b$ is the imaginary part of the complex number.
We have given a complex number $4 + 3i$, then the real part of this complex number is $4$ and the complex part of this number is $3$.
In the case of a complex plane, the $x -$ axis is denoted as the real part of the complex number and $y -$axis is denoted as the imaginary part of the complex number.

The ordered pair to plot this complex number is $\left( {4,3} \right)$.
Notice the values of the both coordinates are positive.
We know that,
First quadrant → $\left( {x,y} \right)$ [Both $x$ and $y$ coordinate are positive]
Second quadrant → $\left( { - x,y} \right)$ [$x$ is negative, $y$ is positive]
Third quadrant → $\left( { - x, - y} \right)$ [Both $x$ and $y$ are negative]
Fourth quadrant → $\left( {x, - y} \right)$ [$x$ is positive, $y$ is negative]
Hence, $4 + 3i$ lies in the first quadrant.

Note: The complex plane is the same as the Cartesian plane, the real part of the complex number is equivalent to the x-axis and the imaginary part of the complex number is equivalent to the y-axis.