Chapter 4, Problem 24CT

Solution

To compare: Graphing a number on the complex plane to graphing a point on the coordinate plane also state their similarities and differences.

Similarity: The real numbers are considered on the horizontal axis in both the planes.

Difference: In the complex plane the imaginary numbers are purely considered on the y -axis on the other hand the real numbers are considered on the y -axis in a coordinate plane.

Given information:

The given statement says to compare the complex plane and the coordinate plane.

Explanation:

If a point is taken as $\left(a,b\right)$ then it represents a complex number $a+ib$ in a complex number plane.

Now to graph this complex number, locate the real part on the x -axis and the imaginary part on the y -axis.

Now locate the point $z=a+ib$ on the complex plane as shown below:

  

If a point is taken as $\left(a,b\right)$ then it represents a real number $a\text{and}b$ in a coordinate number plane.

Now to graph this real number, locate the real points on the x -axis and on the y -axis.

  

Similarities between complex plane and coordinate plane:

In both the planes, the complex plane and the real plane, the real numbers are considered on the horizontal axis.

Differences between complex plane and coordinate plane:

In the complex plane the imaginary numbers are purely considered on the y -axis and in case of the real plane the real numbers are considered on the y -axis.