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Example Questions
Example Question #3 : Graphing
Point A represents a complex number. Its position is given by which of the following expressions?
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 #4 : Graphing
Which of the following graphs represents the expression ?
Complex numbers cannot be represented on a coordinate plane.
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 #171 : Coordinate Geometry
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.
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 #1061 : Problem Solving Questions
In which quadrant does the complex number lie?
-axis
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 #1 : How To Graph Complex Numbers
In which quadrant does the complex number lie?
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 #1062 : Problem Solving Questions
In which quadrant does the complex number lie?
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 #1 : How To Graph Complex Numbers
In which quadrant does the complex number lie?
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 : How To Graph Complex Numbers
In the complex plane, what number does this point represent?
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.
Example Question #1 : How To Graph Complex Numbers
The graph below represents which complex number?
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.
Example Question #1 : How To Graph Complex Numbers
Find,
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.
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