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Chapter 7: Problem 93

Explain how to plot a complex number in the complex plane. Provide an example with your explanation.

Short Answer

Expert verified
A complex number like \(3+4i\) can be represented visually in a complex plane by treating it as a point in two dimensions, where '3' the real part is the x-coordinate and '4' the imaginary part is the y-coordinate. To plot, move 3 units to the right along the real (horizontal) axis from the origin and then move 4 units upwards along the imaginary (vertical) axis. Mark this point, which represents \(3+4i\).

Step by step solution

01

Understand Complex Plane

Before plotting complex numbers, it is important to understand the structure of a complex plane. Unlike the Cartesian plane which has X and Y axes, a complex plane is slightly different. It has a real axis (horizontal) and an imaginary axis (vertical). Each complex number can be represented as a point in this plane, where the real part is the x-coordinate and the imaginary part is the y-coordinate.
02

Identify Real and Imaginary Parts

Next step is identifying the real and imaginary parts of a complex number. Suppose we have an example of a complex number, say \(3 + 4i\), the real part will be '3' and the imaginary part, removed from the imaginary unit 'i', will be '4'.
03

Plot the point in Complex Plane

Next, plot the complex number on the complex plane. As identified, the real part '3' is the x-coordinate and the imaginary part '4' is the y-coordinate. Starting from the origin, move 3 units to the right along the real axis (horizontal axis), and then move 4 units upwards along the imaginary axis (vertical axis). Mark this point, which represents the complex number \(3+4i\) on the complex plane.

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