Graph |z| > 3 on the Complex Plane: A Detailed Explanation

[Raerin]

I have no idea where to post this.

How to graph |z| > 3 on the complex plane? A detailed explanation of how the graph shall look like would be very nice :D

Thanks!

 

[Petrus]

Hello,
|z| means length of z from origin, so the length of the circle is greater Then 3
Regards,
\(\displaystyle |\pi\rangle\)

 

[Raerin]

I understand that, but I have no idea how the graph should look like. I don't know how to draw it to illustrate that the radius is greater than 3.

 

[topsquark]

I understand that, but I have no idea how the graph should look like. I don't know how to draw it to illustrate that the radius is greater than 3.

I think the simplest way to graph this is to draw the circle |z| = 3, then shade the outside of the circle. It's not perfect, but it gets the idea across.

-Dan

 

[CellCoree]

I would be happy to provide a detailed explanation on how to graph |z| > 3 on the complex plane. First, let's define what |z| means. In the complex plane, z represents a complex number, which has a real part (a) and an imaginary part (bi). The absolute value or modulus of a complex number is denoted by |z| and is defined as the distance from the origin (0+0i) to the point representing the complex number. This can be calculated using the Pythagorean theorem as |z| = √(a^2+b^2).

Now, let's focus on the inequality |z| > 3. This means that the distance from the origin to the point representing the complex number z is greater than 3. To graph this on the complex plane, we will use the Cartesian coordinate system where the horizontal axis represents the real numbers and the vertical axis represents the imaginary numbers.

To begin, draw the x and y axes intersecting at the origin. The point (3,0) on the x-axis represents a complex number with a real part of 3 and an imaginary part of 0. Similarly, the point (0,3) on the y-axis represents a complex number with a real part of 0 and an imaginary part of 3. These two points form a square with the origin as its center.

Next, we need to shade the region outside of this square to represent the points that satisfy the inequality |z| > 3. This is because all the points outside of the square have a distance greater than 3 from the origin.

To further visualize this, we can also plot a few points on the graph. For example, the point (4,2) represents a complex number with a distance of √(4^2+2^2) = √20 > 3 from the origin. Similarly, the point (-2,-2) represents a complex number with a distance of √((-2)^2+(-2)^2) = √8 > 3 from the origin.

Overall, the graph of |z| > 3 on the complex plane will look like a shaded region outside of a square centered at the origin. I hope this explanation helps you understand how to graph this inequality on the complex plane.