# Precalculus : Find the Product of Complex Numbers

## Example Questions

### Example Question #1 : Polar Coordinates And Complex Numbers

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 : Find The Product Of 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 #1 : 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 : Polar Coordinates And Complex Numbers

Compute the magnitude of .      Explanation:

We have We know that Thus this gives us, .

### Example Question #2 : Products And Quotients Of Complex Numbers In Polar Form

Evaluate:       Explanation:

To evaluate this problem we need to FOIL the binomials.   Now recall that Thus,  ### Example Question #1 : Find The Product Of 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 . The correct answer is: ### Example Question #1 : Products And Quotients Of Complex Numbers In Polar Form

Find the product of the two complex numbers and      Explanation:

The product is ### All Precalculus Resources 