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Example Questions
Example Question #1 : Find The Product Of Complex Numbers
Find the value of ,where
the complex number is given by
.
We note that by FOILing.
We also know that:
We have by using the above rule: n=2 , m=50
Since we know that,
We have then:
Since we know that:
, we use a=2 ,b=i
We have then:
Example Question #1 : Polar Coordinates And Complex Numbers
Compute the following sum:
. Remember
is the complex number satisfying
.
Note that this is a geometric series.
Therefore we have:
Note that,
=
and since
we have
.
this shows that the sum is 0.
Example Question #1 : Products And Quotients Of Complex Numbers In Polar Form
Find the following product.
Note that by FOILing the two binomials we get the following:
Therefore,
Example Question #4 : Find The Product Of Complex Numbers
Compute the magnitude of .
We have
.
We know that
Thus this gives us,
.
Example Question #1 : Polar Coordinates And Complex Numbers
Evaluate:
To evaluate this problem we need to FOIL the binomials.
Now recall that
Thus,
Example Question #1 : Polar Coordinates And Complex Numbers
Find the product , if
.
To find the product , FOIL the complex numbers. FOIL stands for the multiplication of the Firsts, Outers, Inners, and Lasts.
Using this method we get the following,
and because
.
Example Question #1 : Polar Coordinates And Complex Numbers
Simplify:
The expression can be rewritten as:
Since , the value of
.
The correct answer is:
Example Question #1 : Polar Coordinates And Complex Numbers
Find the product of the two complex numbers
and
The product is
Example Question #1 : Find The Quotient Of Complex Numbers
Let ,
. Find a simple form of
.
We remark first that:
and we know that :
.
This means that:
Example Question #1 : Products And Quotients Of Complex Numbers In Polar Form
What is ?
Since ,
the problem becomes,
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