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:

In the complex plane, the x-axis represents the real component of the complex number, and the y-axis represents the imaginary part. The point shown is (8,3) so the real part is 8 and the imaginary part is 3, or 8+3i.

For the answer we must know that the x-axis is the real axis and the y-axis is the imaginary axis. We can see that we have gone 2 spaces in the x-axis or real direction and -3 spaces in the y-axis or imaginary direction to give us the answer 2-3i. 

The definition of Absolute Value on a coordinate plane is the distance from the origin to the point. 

When graphing this complex number, you would go 3 spaces right (real axis is the x-axis) and 4 spaces down (the imaginary axis is the y-axis). 

This forms a right triangle with legs of 3 and 4. 

To solve, plug in each directional value into the Pythagorean Theorem. 

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. 

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

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.

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 add two complex numbers, add the real parts and add the imaginary parts:

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:

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):