### All ACT Math Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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 #1 : How To Graph Complex Numbers

Point A represents a complex number. Its position is given by which of the following expressions?

**Possible Answers:**

**Correct answer:**

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 #3 : How To Graph Complex Numbers

Which of the following graphs represents the expression ?

**Possible Answers:**

Complex numbers cannot be represented on a coordinate plane.

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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 .