Precalculus : Find the Product of Complex Numbers

Study concepts, example questions & explanations for Precalculus

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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 .

Possible Answers:

Correct answer:

Explanation:

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 #2 : Find The Product Of Complex Numbers

Compute the following sum:

. Remember  is the complex number satisfying .

Possible Answers:

Correct answer:

Explanation:

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 #3 : Find The Product Of Complex Numbers

Find the following product.

Possible Answers:

Correct answer:

Explanation:

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 .

Possible Answers:

Correct answer:

Explanation:

We have

We know that 

Thus this gives us,

.

Example Question #1 : Find The Product Of Complex Numbers

Evaluate:

Possible Answers:

Correct answer:

Explanation:

To evaluate this problem we need to FOIL the binomials.

Now recall that 

Thus,

Example Question #6 : Find The Product Of Complex Numbers

Find the product , if

.

Possible Answers:

Correct answer:

Explanation:

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 #7 : Find The Product Of Complex Numbers

Simplify:  

Possible Answers:

Correct answer:

Explanation:

The expression  can be rewritten as:

Since , the value of .

The correct answer is:  

Example Question #2 : Find The Product Of Complex Numbers

Find the product of the two complex numbers

  and 

Possible Answers:

Correct answer:

Explanation:

The product is

 

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