How to graph complex numbers - ACT Math
Card 0 of 4
Point A represents a complex number. Its position is given by which of the following expressions?
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 
.
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
Here, we are given the graph and asked to write the corresponding expression.
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Which of the following graphs represents the expression 
?
Which of the following graphs represents the expression
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 
.
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
Here, we are given the complex number
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The graph of 
passes through 
in the standard 
coordinate plane. What is the value of 
?
The graph of
To answer this question, we need to correctly identify where to plug in our given values and solve for 
.
Points on a graph are written in coordinate pairs. These pairs show the 
value first and the 
value second. So, for this data:
means that 
is the 
value and 
is the 
value.
We must now plug in our and values into the original equation and solve. Therefore:
We can now begin to solve for 
by adding up the right side and dividing the entire equation by 
.
Therefore, the value of 
is 
.
To answer this question, we need to correctly identify where to plug in our given values and solve for
Points on a graph are written in coordinate pairs. These pairs show the
We must now plug in our
We can now begin to solve for
Therefore, the value of
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The point 
is on the graph of 
. What is the value of 
?
The point
Because points on a graph are written in the form of 
, and the point given was 
, this means that 
and 
.
In order to solve for 
, these values for 
and 
must be plugged into the given equation. This gives us the following:
We then solve the equation by finding the value of the right side, then dividing the entire equation by 5, as follows:
Therefore, the value of 
is 
.
Because points on a graph are written in the form of
In order to solve for
We then solve the equation by finding the value of the right side, then dividing the entire equation by 5, as follows:
Therefore, the value of
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