All Precalculus Resources
Example Questions
Example Question #1 : Products And Quotients Of Complex Numbers In Polar Form
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 : Polar Coordinates And Complex Numbers
Find the following product.
Note that by FOILing the two binomials we get the following:
Therefore,
Example Question #1 : Find The Product Of Complex Numbers
Compute the magnitude of .
We have
.
We know that
Thus this gives us,
.
Example Question #4 : Find The Product Of Complex Numbers
Evaluate:
To evaluate this problem we need to FOIL the binomials.
Now recall that
Thus,
Example Question #5 : Find The Product Of 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 #6 : Find The Product Of Complex Numbers
Simplify:
The expression can be rewritten as:
Since , the value of .
The correct answer is:
Example Question #3 : Polar Coordinates And Complex Numbers
Find the product of the two complex numbers
and
The product is
Example Question #3 : Products And Quotients Of Complex Numbers In Polar Form
Let , . Find a simple form of .
We remark first that:
and we know that :
.
This means that:
Example Question #1 : Find The Quotient Of Complex Numbers
What is ?
Since ,
the problem becomes,