Graphing Complex Numbers: Videos & Practice Problems

To plot complex numbers on a complex plane, identify the real and imaginary parts. The real part corresponds to the horizontal axis, while the imaginary part corresponds to the vertical axis. For example, the complex number $3+2i$ is plotted by moving 3 units right and 2 units up. Similarly, $2-4i$ moves 2 units right and 4 units down. Understanding this process is essential for visualizing complex numbers effectively.

How To Plot Complex Numbers

Understanding how to plot complex numbers on a graph is essential for visualizing their properties. Complex numbers are expressed in the form x + yi, where x represents the real part and y represents the imaginary part. To plot these numbers, we utilize a complex plane, which consists of a real axis (horizontal) and an imaginary axis (vertical).

When plotting a complex number, the real part indicates the position along the real axis, while the imaginary part indicates the position along the imaginary axis. For example, to plot the complex number 3 + 2i, you would move 3 units to the right on the real axis and 2 units up on the imaginary axis, placing the point at the intersection of these two movements.

In another example, for the complex number 2 - 4i, the real part is 2, so you move 2 units to the right. The imaginary part is -4, indicating a movement of 4 units down. Thus, the point is plotted accordingly. If you encounter a complex number like 3i, it can be rewritten as 0 + 3i, indicating that the real part is 0 and the imaginary part is 3. This means you stay at the origin on the real axis and move 3 units up on the imaginary axis.

In summary, plotting complex numbers involves identifying the real and imaginary components and translating them into movements on the complex plane. This process is straightforward and mirrors the plotting of points on a standard x-y graph, allowing for a clear representation of complex numbers in a two-dimensional space.

Plot the complex number $z=2-4i$ on the graph below.

• A.
• B.
• C.
• D.

Answer: (B)

Plot the complex number $z=-i$ on the graph below.

• A.
• B.
• C.
• D.

Answer: (C)

Plot the complex number $z=5$ on the graph below.

• A.
• B.
• C.
• D.

Answer: (A)

Here’s what students ask on this topic:

How do you plot complex numbers on a complex plane?

To plot complex numbers on a complex plane, identify the real and imaginary parts of the number. The real part corresponds to the horizontal axis (real axis), and the imaginary part corresponds to the vertical axis (imaginary axis). For example, to plot the complex number 3+2i, move 3 units to the right on the real axis and 2 units up on the imaginary axis. Similarly, for 2-4i, move 2 units to the right and 4 units down. This method helps visualize complex numbers effectively.

What is the complex plane in graphing complex numbers?

The complex plane is a two-dimensional plane used to graph complex numbers. It consists of a horizontal axis called the real axis and a vertical axis called the imaginary axis. Each complex number is represented as a point on this plane, where the real part determines the position along the real axis and the imaginary part determines the position along the imaginary axis. This plane helps in visualizing and understanding the properties of complex numbers.

How do you plot the complex number 3i on a complex plane?

To plot the complex number 3i on a complex plane, recognize that it can be written as 0+3i. The real part is 0, and the imaginary part is 3. Since the real part is 0, you do not move left or right on the real axis. For the imaginary part, move 3 units up on the imaginary axis. The point representing 3i will be located at (0, 3) on the complex plane.

What are the steps to plot the complex number 2-4i?

To plot the complex number 2-4i on a complex plane, follow these steps: 1) Identify the real part (2) and the imaginary part (-4). 2) Move 2 units to the right on the real axis. 3) Move 4 units down on the imaginary axis. The point where these movements intersect represents the complex number 2-4i on the complex plane.

What is the difference between the real axis and the imaginary axis in a complex plane?

In a complex plane, the real axis is the horizontal axis, and it represents the real part of a complex number. The imaginary axis is the vertical axis, and it represents the imaginary part of a complex number. When plotting a complex number, the real part determines the position along the real axis, while the imaginary part determines the position along the imaginary axis. This distinction helps in visualizing complex numbers as points in a two-dimensional space.