General Contents
Detailed Contents
Index
Complex Plane or Argand Diagram: Example 2
If you find this page helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
If you want to see all of the following steps at once, click the "All Steps" button. Otherwise, use the "Next" button.
Interpret the point
as a complex number.
For background see this
link
.
Which part of the complex number do we associate
with the
x
–axis?
The real part.
Which number is that here?
The
.
Which part of the complex number do we associate
with the
y
–axis?
The imaginary part.
Which number is that here?
The 1.
Plot this complex number in the complex plane.
alt="Your browser understands the <APPLET> tag but isn't running the applet, for some reason." Your browser is completely ignoring the <APPLET> tag!
Note the blue indicating the real part and the green indicating the imaginary part of this complex number.
What is the name associated with "r" on the graph?
It is the modulo of the complex number.
What is the name associated with "phi" on the graph?
It is the argument of the complex number.
How is the modulo related to the
x
– and
y
– coordinates?
Using the Pythagorean theorem we get
How is the argument related to the
x
– and
y
– coordinates?
How do we solve for
?
We apply the inverse tangent function to each side of the equation.
Set that up.
Simplify the left side.
We get
Find the modulo for this problem.
Find the argument for this problem.
Recall that the range of the arctan is
Is this consistent with the diagram?
No.
How can we make it consistent?
We can use the fact that the tangent is negative in the second quadrant also.
Use that fact to determine
phi
.
Interpret this complex number as
.
What is the value of
a
?
What is the value of
b
?
Combine these results to write the complex number.
We get
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
Email to John Taylor
General Contents
Detailed Contents
Index