# High School Math : Understanding Imaginary and Complex Numbers

## Example Questions

### Example Question #21 : Algebra Ii

Simplify the radical.

Possible Answers:

No solution

Correct answer:

Explanation:

First, factor the term in the radical.

Now, we can simplify.

### Example Question #1 : Imaginary Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

FOIL:

### Example Question #23 : Algebra Ii

Multiply:

Possible Answers:

Correct answer:

Explanation:

Since  and  are conmplex conjugates, they can be multiplied according to the following pattern:

### Example Question #24 : Algebra Ii

Multiply:

Possible Answers:

Correct answer:

Explanation:

Since  and  are conmplex conjugates, they can be multiplied according to the following pattern:

### Example Question #25 : Algebra Ii

Evaluate:

Possible Answers:

Correct answer:

Explanation:

can be evaluated by dividing  by 4 and noting the remainder. Since  - that is, since dividing 45 by 4 yields remainder 1:

### Example Question #1 : Understanding Imaginary And Complex Numbers

Evaluate:

Possible Answers:

Correct answer:

Explanation:

### Example Question #1 : Basic Operations With Complex Numbers

What is the absolute value of

Possible Answers:

Correct answer:

Explanation:

The absolute value is a measure of the distance of a point from the origin.  Using the pythagorean distance formula to calculate this distance.

### Example Question #2 : Understanding Imaginary And Complex Numbers

Which of the following is equivalent to:

Possible Answers:

Correct answer:

Explanation:

Recall that

Then, we have that .

Note that we used the power rule of exponents and the order of operations to simplify the exponent before multiplying by the coefficient.

### Example Question #1 : Basic Operations With Complex Numbers

Simplify the expression.

Possible Answers:

None of the other answer choices are correct.

Correct answer:

Explanation:

Combine like terms. Treat as if it were any other variable.

Substitute to eliminate .

Simplify.

### Example Question #3 : Understanding Imaginary And Complex Numbers

Which of the following is equivalent to  ?

Possible Answers:

None of the other answer choices are correct.

Correct answer:

Explanation:

Recall the basic property of imaginary numbers, .

Keeping this in mind, .