Find the Product of Complex Numbers - Pre-Calculus
Card 0 of 32
Find the value of
,where
the complex number is given by
.
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:

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:
Compare your answer with the correct one above
Compute the following sum:
. Remember
is the complex number satisfying
.
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.
Note that this is a geometric series.
Therefore we have:
Note that,
=
and since
we have
.
this shows that the sum is 0.
Compare your answer with the correct one above
Find the following product.

Find the following product.
Note that by FOILing the two binomials we get the following:

Therefore,

Note that by FOILing the two binomials we get the following:
Therefore,
Compare your answer with the correct one above
Compute the magnitude of
.
Compute the magnitude of .
We have
.
We know that 
Thus this gives us,
.
We have
.
We know that
Thus this gives us,
.
Compare your answer with the correct one above
Evaluate:

Evaluate:
To evaluate this problem we need to FOIL the binomials.



Now recall that 
Thus,


To evaluate this problem we need to FOIL the binomials.
Now recall that
Thus,
Compare your answer with the correct one above
Find the product
, if
.
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 
.
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
.
Compare your answer with the correct one above
Simplify: 
Simplify:
The expression
can be rewritten as:

Since
, the value of
.

The correct answer is: 
The expression can be rewritten as:
Since , the value of
.
The correct answer is:
Compare your answer with the correct one above
Find the product of the two complex numbers
and 
Find the product of the two complex numbers
and
The product is

The product is
Compare your answer with the correct one above
Find the value of
,where
the complex number is given by
.
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:

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:
Compare your answer with the correct one above
Compute the following sum:
. Remember
is the complex number satisfying
.
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.
Note that this is a geometric series.
Therefore we have:
Note that,
=
and since
we have
.
this shows that the sum is 0.
Compare your answer with the correct one above
Find the following product.

Find the following product.
Note that by FOILing the two binomials we get the following:

Therefore,

Note that by FOILing the two binomials we get the following:
Therefore,
Compare your answer with the correct one above
Compute the magnitude of
.
Compute the magnitude of .
We have
.
We know that 
Thus this gives us,
.
We have
.
We know that
Thus this gives us,
.
Compare your answer with the correct one above
Evaluate:

Evaluate:
To evaluate this problem we need to FOIL the binomials.



Now recall that 
Thus,


To evaluate this problem we need to FOIL the binomials.
Now recall that
Thus,
Compare your answer with the correct one above
Find the product
, if
.
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 
.
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
.
Compare your answer with the correct one above
Simplify: 
Simplify:
The expression
can be rewritten as:

Since
, the value of
.

The correct answer is: 
The expression can be rewritten as:
Since , the value of
.
The correct answer is:
Compare your answer with the correct one above
Find the product of the two complex numbers
and 
Find the product of the two complex numbers
and
The product is

The product is
Compare your answer with the correct one above
Find the value of
,where
the complex number is given by
.
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:

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:
Compare your answer with the correct one above
Compute the following sum:
. Remember
is the complex number satisfying
.
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.
Note that this is a geometric series.
Therefore we have:
Note that,
=
and since
we have
.
this shows that the sum is 0.
Compare your answer with the correct one above
Find the following product.

Find the following product.
Note that by FOILing the two binomials we get the following:

Therefore,

Note that by FOILing the two binomials we get the following:
Therefore,
Compare your answer with the correct one above
Compute the magnitude of
.
Compute the magnitude of .
We have
.
We know that 
Thus this gives us,
.
We have
.
We know that
Thus this gives us,
.
Compare your answer with the correct one above