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
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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
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 have then:
Compute the following sum:
. Remember 
is the complex number satisfying 
.
Compute the following sum:
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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,
this shows that the sum is 0.
Find the following product.
Find the following product.
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Note that by FOILing the two binomials we get the following:
Therefore,
Note that by FOILing the two binomials we get the following:
Therefore,
Compute the magnitude of 
.
Compute the magnitude of
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We have
.
We know that 
Thus this gives us,
.
We have
We know that
Thus this gives us,
Evaluate:
Evaluate:
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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,
Find the product 
, if
.
Find the product
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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
Using this method we get the following,
and because
Simplify: 
Simplify:
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The expression 
can be rewritten as:
Since 
, the value of 
.
The correct answer is: 
The expression
Since
The correct answer is:
Find the product of the two complex numbers
and 
Find the product of the two complex numbers
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The product is
The product is
Find the value of ,where the complex number is given by .
Find the value of
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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
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 have then:
Compute the following sum:
. Remember is the complex number satisfying .
Compute the following sum:
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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,
this shows that the sum is 0.
Find the following product.
Find the following product.
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Note that by FOILing the two binomials we get the following:
Therefore,
Note that by FOILing the two binomials we get the following:
Therefore,
Compute the magnitude of .
Compute the magnitude of
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We have
.
We know that
Thus this gives us,
.
We have
We know that
Thus this gives us,
Evaluate:
Evaluate:
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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,
Find the product , if
.
Find the product
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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
Using this method we get the following,
and because
Simplify:
Simplify:
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The expression can be rewritten as:
Since , the value of .
The correct answer is:
The expression
Since
The correct answer is:
Find the product of the two complex numbers
and
Find the product of the two complex numbers
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The product is
The product is
Find the value of ,where the complex number is given by .
Find the value of
Tap to see back →
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
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 have then:
Compute the following sum:
. Remember is the complex number satisfying .
Compute the following sum:
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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,
this shows that the sum is 0.
Find the following product.
Find the following product.
Tap to see back →
Note that by FOILing the two binomials we get the following:
Therefore,
Note that by FOILing the two binomials we get the following:
Therefore,
Compute the magnitude of .
Compute the magnitude of
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We have
.
We know that
Thus this gives us,
.
We have
We know that
Thus this gives us,