### All High School Math Resources

## Example Questions

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

Simplify the radical.

**Possible Answers:**

No solution

**Correct answer:**

First, factor the term in the radical.

Now, we can simplify.

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

Multiply:

**Possible Answers:**

**Correct answer:**

FOIL:

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

Multiply:

**Possible Answers:**

**Correct answer:**

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

### Example Question #4 : Understanding Imaginary And Complex Numbers

Multiply:

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : Understanding Imaginary And Complex Numbers

Evaluate:

**Possible Answers:**

**Correct answer:**

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

### Example Question #6 : Understanding Imaginary And Complex Numbers

Evaluate:

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Understanding Imaginary And Complex Numbers

What is the absolute value of

**Possible Answers:**

**Correct answer:**

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 #8 : Understanding Imaginary And Complex Numbers

Which of the following is equivalent to:

**Possible Answers:**

**Correct answer:**

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 #9 : Understanding Imaginary And Complex Numbers

Simplify the expression.

**Possible Answers:**

None of the other answer choices are correct.

**Correct answer:**

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

Substitute to eliminate .

Simplify.

### Example Question #10 : Understanding Imaginary And Complex Numbers

Which of the following is equivalent to ?

**Possible Answers:**

None of the other answer choices are correct.

**Correct answer:**

Recall the basic property of imaginary numbers, .

Keeping this in mind, .

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