Select the graph that would represent the best presentation of the solution set for |z| > (1/2).
The graph that would represent the best presentation of the solution set for |z| > (1/2) is Option C, which is a shaded region outside the circle with radius 1/2 centered at the origin.
To represent the solution set for |z| > (1/2), we need to use a graph that can represent complex numbers. The best graph to represent complex numbers is the Argand diagram or complex plane.
In the complex plane, the real part of the complex number is represented on the horizontal axis (x-axis) and the imaginary part is represented on the vertical axis (y-axis). The origin of the graph represents the complex number 0.
To represent |z| > (1/2), we need to plot all the complex numbers that have a magnitude greater than (1/2) on the graph. This means that the distance of each complex number from the origin must be greater than (1/2).
To do this, we can shade the region outside the circle centered at the origin with a radius of (1/2).
Here is the step-by-step process to draw the graph:
1. Draw the x-axis and y-axis on the graph paper.
2. Mark the origin (0,0) at the center of the graph.
3. Draw a circle centered at the origin with a radius of (1/2). You can use a compass or any circular object with a diameter of 1 unit to draw this circle.
4. Shade the region outside the circle, including the circumference. This shaded region represents the solution set |z| > (1/2).
The graph will consist of a shaded region outside the circle centered at the origin with a radius of (1/2).
Note: The shading is done because the magnitude of each complex number greater than (1/2) lies outside the circle.
To select the graph that represents the solution set for the inequality |z| > 1/2, we need to understand what this inequality means in the context of the complex plane.
The inequality |z| > 1/2 translates to "the modulus of z is greater than 1/2." Modulus, also known as absolute value, measures the distance of a complex number from the origin (0, 0) in the complex plane.
In this case, we need to find the set of complex numbers that are at a distance greater than 1/2 from the origin. This set forms a region in the complex plane.
To represent this region graphically, we can use a graph that shades the area outside the circle centered at the origin with a radius of 1/2. Since the inequality is strict (|z| > 1/2), the circle should not be included in the solution set.
Therefore, the best graph that represents the solution set for |z| > 1/2 is an open circle at the origin with a radius of 1/2, and the region shaded outside this circle.
Here is an ASCII representation of what the graph would look like:
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/ \
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The shaded area represents the solution set for |z| > 1/2.