### All Precalculus Resources

## Example Questions

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

Find the value of ,where the complex number is given by .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

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:**

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:**

We have

.

We know that

Thus this gives us,

.

### Example Question #3 : Polar Coordinates And Complex Numbers

Evaluate:

**Possible Answers:**

**Correct answer:**

To evaluate this problem we need to FOIL the binomials.

Now recall that

Thus,

### Example Question #2 : Find The Product Of Complex Numbers

Find the product , if

.

**Possible Answers:**

**Correct answer:**

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 #3 : Polar Coordinates And Complex Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

The expression can be rewritten as:

Since , the value of .

The correct answer is:

### Example Question #3 : Find The Product Of Complex Numbers

Find the product of the two complex numbers

and

**Possible Answers:**

**Correct answer:**

The product is

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