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Example Questions
Example Question #11 : Complex Numbers
Evaluate:
The general formula to figure out the modulus is
We apply this to get
Example Question #12 : Complex Numbers
Evaluate:
The general formula to figure out the modulus is
.
We apply this notion to get.
Example Question #13 : Complex Numbers
Evaluate
None of the other answers
-64
-64i
64i
64
-64
Converting from rectangular to polar coordinates gives us
So
Example Question #14 : Complex Numbers
Compute
Converting from Rectangular to Polar Coordinates
Evaluating for
we get that
Example Question #15 : Complex Numbers
The 5th roots of unity are the five unique solutions to which equation?
None of these
A 5th root of unity is a complex number such that
. Manipulating this equation yields
.
Example Question #16 : Complex Numbers
What is the magnitude of the following complex number?
None of these
The magnitude of a complex number is defined as
So the modulus of is
.
Example Question #14 : Complex Numbers
What is the magnitude of the following complex number?
None of these
The magnitude of a complex number is defined as
So the modulus of is
.
Example Question #17 : Complex Numbers
What is the magnitude of the following complex number?
None of these
The magnitude of a complex number is defined as
Because the complex number has no imaginary part, we can write it in the form
. Then the modulus of
is
.
Example Question #18 : Complex Numbers
What is the argument of the following complex number?
None of these
Note that the complex number lies in the first quadrant of the complex plane.
For a complex number , the argument of
is defined as the real number
such that
,
where is in radians.
Then the argument of is
.
The angle lies in the third quadrant of the complex plane, but the angle
lies in the first quadrant, as does
. So
.
Example Question #19 : Complex Numbers
What is the argument of the following complex number in radians, rounded to the nearest hundredth?
None of these
Note that the complex number lies in the fourth quadrant of the complex plane.
For a complex number , the argument of
is defined as the real number
such that
,
where is in radians.
Then the argument of is
.
The angle lies in the second quadrant of the complex plane, but the angle
lies in the fourth quadrant, as does
. So
.
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