# Precalculus : Find the Product of Complex Numbers

## 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 .

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 #1 : Polar Coordinates And Complex Numbers

Compute the following sum:

. Remember  is the complex number satisfying .

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 #2 : Polar Coordinates And Complex Numbers

Find the following product.

Explanation:

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 .

Explanation:

We have

We know that

Thus this gives us,

.

### Example Question #1 : Find The Product Of Complex Numbers

Evaluate:

Explanation:

To evaluate this problem we need to FOIL the binomials.

Now recall that

Thus,

### Example Question #4 : Polar Coordinates And Complex Numbers

Find the product , if

.

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 #1 : Polar Coordinates And Complex Numbers

Simplify:

Explanation:

The expression  can be rewritten as:

Since , the value of .

### Example Question #1 : Products And Quotients Of Complex Numbers In Polar Form

Find the product of the two complex numbers

and