# Advanced Geometry : How to graph complex numbers

## Example Questions

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### Example Question #11 : How To Graph Complex Numbers

Explanation:

In the complex plane, the imaginary axis matches the y-axis and the real axis matches the x-axis.

When graphing complex numbers, we go left or right to graph the real number and then up or down to graph the complex number.

### Example Question #12 : How To Graph Complex Numbers

Refer to the above diagram, which shows four points on the complex plane.

Select the point which gives the result of the addition

Explanation:

On the complex plane, a complex number whose real part is negative is left of the imaginary (vertical) axis; a complex number whose imaginary coefficient is positive is above the real (horizontal axis).  is three units left of and five units above the origin; this is point A.

### Example Question #13 : How To Graph Complex Numbers

Refer to the above diagram, which shows two points on the complex plane. Let  and  stand for the complex numbers represented by their respective points.

None of the other choices gives the correct response.

Explanation:

On the complex plane, the real and imaginary parts of a point are equal to the horizontal and vertical distances, respectively, from the origin to the point, with the right and upward directions representing positive quantities and the left and downward directions representing negative quantities. Refer to the diagram below, which shows the horizontal and vertical distances from the origin of both points.

is six units right of the origin, representing real part 6, and eight units above the origin, representing imaginary part  is two units right of the origin, representing real part 2, and five units below the origin, representing imaginary part . Therefore,

We are asked to find .

### Example Question #14 : How To Graph Complex Numbers

Refer to the above diagram, which shows two points on the complex plane. Let  and  stand for the complex numbers represented by their respective points.

Subtract  from .

None of the other choices gives the correct response.

Explanation:

On the complex plane, the real and imaginary parts of a point are equal to the horizontal and vertical distances, respectively, from the origin to the point, with the right and upward directions representing positive quantities and the left and downward directions representing negative quantities. Refer to the diagram below, which shows the horizontal and vertical distances from the origin of both points.

is six units right of the origin, representing real part 6, and eight units above the origin, representing imaginary part  is two units right of the origin, representing real part 2, and five units below the origin, representing imaginary part . Therefore,

We are asked to find .

To subtract two complex numbers, subtract the real parts and subtract the imaginary parts:

### Example Question #15 : How To Graph Complex Numbers

Refer to the above diagram, which shows two points on the complex plane. Let  and  stand for the complex numbers represented by their respective points.

Multiply  by .

Explanation:

On the complex plane, the real and imaginary parts of a point are equal to the horizontal and vertical distances, respectively, from the origin to the point, with the right and upward directions representing positive quantities and the left and downward directions representing negative quantities. Refer to the diagram below, which shows the horizontal and vertical distances from the origin of both points.

is six units right of the origin, representing real part 6, and eight units above the origin, representing imaginary part  is two units right of the origin, representing real part 2, and five units below the origin, representing imaginary part . Therefore,

To multiply two complex numbers, use the FOIL method as if you were multiplying two binomials.

F(irst):

O(uter):

I(nner):

L(ast):

By definition, , so the "L" quantity simplifies:

.

Add these quantities, collecting real parts (F and L) and imaginary parts (O and I):

### Example Question #16 : How To Graph Complex Numbers

Refer to the above diagram, which shows four points on the complex plane.

Select the point which gives the result of the subtraction

.