# GMAT Math : Graphing complex numbers

## Example Questions

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

Give the -intercept(s) of the parabola with equation . Round to the nearest tenth, if applicable.

The parabola has no  -intercept.

The parabola has no  -intercept.

Explanation:

The -coordinate(s) of the -intercept(s) are the real solution(s) to the equation . We can use the quadratic formula to find any solutions, setting  - the coefficients of the expression.

An examination of the discriminant , however, proves this unnecessary.

The discriminant being negative, there are no real solutions, so the parabola has no  -intercepts.

### Example Question #4 : How To Graph Complex Numbers

In which quadrant does the complex number    lie?

-axis

Explanation:

When plotting a complex number, we use a set of real-imaginary axes in which the x-axis is represented by the real component of the complex number, and the y-axis is represented by the imaginary component of the complex number. The real component is    and the imaginary component is  ,  so this is the equivalent of plotting the point    on a set of Cartesian axes.  Plotting the complex number on a set of real-imaginary axes, we move    to the left in the x-direction and    up in the y-direction, which puts us in the second quadrant, or in terms of Roman numerals:

### Example Question #5 : How To Graph Complex Numbers

In which quadrant does the complex number    lie?

Explanation:

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 in the x direction, and    units down in the y direction, which puts us in the fourth quadrant, or in terms of Roman numerals:

### Example Question #6 : How To Graph Complex Numbers

In which quadrant does the complex number    lie?

Explanation:

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:

### Example Question #7 : How To Graph Complex Numbers

In which quadrant does the complex number    lie?

Explanation:

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:

### Example Question #1 : Graphing Complex Numbers

Raise  to the power of four.

None of the other responses gives the correct answer.

Explanation:

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:

### Example Question #2 : Graphing Complex Numbers

Raise  to the power of eight.

Explanation:

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:

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