# ACT Math : How to graph complex numbers

## 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 ?

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 #1 : 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 #2 : How To Graph Complex Numbers

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