## Example Questions

### Example Question #7 : Graphing

The graph of passes through in the standard coordinate plane. What is the value of ?      Explanation:

To answer this question, we need to correctly identify where to plug in our given values and solve for .

Points on a graph are written in coordinate pairs. These pairs show the value first and the value second. So, for this data: means that is the value and is the value.

We must now plug in our and values into the original equation and solve. Therefore: We can now begin to solve for by adding up the right side and dividing the entire equation by .  Therefore, the value of is .

### Example Question #8 : Graphing Point A represents a complex number.  Its position is given by which of the following expressions?     Explanation:

Complex numbers can be represented on the coordinate plane by mapping the real part to the x-axis and the imaginary part to the y-axis.  For example, the expression can be represented graphically by the point .

Here, we are given the graph and asked to write the corresponding expression. not only correctly identifies the x-coordinate with the real part and the y-coordinate with the imaginary part of the complex number, it also includes the necessary  correctly identifies the x-coordinate with the real part and the y-coordinate with the imaginary part of the complex number, but fails to include the necessary . misidentifies the y-coordinate with the real part and the x-coordinate with the imaginary part of the complex number. misidentifies the y-coordinate with the real part and the x-coordinate with the imaginary part of the complex number.  It also fails to include the necessary .

### Example Question #1 : How To Graph Complex Numbers

Which of the following graphs represents the expression ?   Complex numbers cannot be represented on a coordinate plane.  Explanation:

Complex numbers can be represented on the coordinate plane by mapping the real part to the x-axis and the imaginary part to the y-axis.  For example, the expression can be represented graphically by the point .

Here, we are given the complex number and asked to graph it.  We will represent the real part, , on the x-axis, and the imaginary part, , on the y-axis.  Note that the coefficient of is ; this is what we will graph on the y-axis.  The correct coordinates are .

### Example Question #1 : How To Graph Complex Numbers

The point is on the graph of . What is the value of ?      Explanation:

Because points on a graph are written in the form of , and the point given was , this means that and .

In order to solve for , these values for and must be plugged into the given equation. This gives us the following:  We then solve the equation by finding the value of the right side, then dividing the entire equation by 5, as follows:     Therefore, the value of is .

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