If we graphed the given complex number on a set of real-imaginary axes, we would plot the real value of the complex number as the x coordinate, and the imaginary value of the complex number as the y coordinate. Because the given complex number is as follows:

We are essentially doing the same as plotting the point    on a set of Cartesian axes.  We move    units left of the origin in the x direction, and    units down from the origin in the y direction, which puts us in the third quadrant, or in terms of Roman numerals:

If we graphed the given complex number on a set of real-imaginary axes, we would plot the real value of the complex number as the x coordinate, and the imaginary value of the complex number as the y coordinate. Because the given complex number is as follows:

We are essentially doing the same as plotting the point    on a set of Cartesian axes.  We move    units right of the origin in the x direction, and    units up from the origin in the y direction, which puts us in the first quadrant, or in terms of Roman numerals:

Squaring an expression, then squaring the result, amounts to taking the original expression to the fourth power. Therefore, we can first square : 

Now square this result:

For any expression , . That is, we can raise an expression to the power of eight by squaring it, then squaring the result, then squaring that result. 

First, we square:

Square this result to obtain the fourth power:

Square this result to obtain the eighth power:

The vertical asymptote is , where  is found by setting the denominator equal to 0 and solving for :

This is the equation of the vertical asymptote.

Set  in the equation and solve for .

This is impossible, so the equation has no solution. Therefore, the graph has no -intercept. 

Set  in the equation and solve for .

The -intercept is 

To find the horizontal asymptote, we can divide both numerator and denominator in the right expression by :

As  approaches positive or negative infinity,  and  both approach 0. Therefore,  approaches , making the horizontal asymptote the line of the equation  .

Set  in the equation:

The -intercept is .

First, we determine the equation of the boundary line. This line includes points  and  , so the slope can be calculated as follows:

We can find the slope-intercept form of the line by substituting  

in the following equation:

The equation of the boundary line is .

The boundary is excluded, as is indicated by the line being dashed, so the equality symbol is replaced by either  or . To find out which one, we can test a point in the solution set - for ease, we will choose :

 _____   

  _____ 

  _____ 

0 is greater than  so the correct symbol is . 

The correct choice is .