# High School Math : Imaginary Numbers

## Example Questions

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### Example Question #41 : Algebra Ii

Simplify the following complex number expression:

Explanation:

Begin by simplifying the radicals using complex numbers:

Multiply the factors:

Simplify. Remember that  is equivalent to .

### Example Question #42 : Algebra Ii

Simplify the following complex number expression:

Explanation:

Begin by completing the square:

Multiply the factors:

Simplify. Remember that  is equivalent to .

### Example Question #43 : Algebra Ii

Simplify the following complex number expression:

Explanation:

Begin by completing the square:

Now, multiply the factors:

Simplify. Remember that  is equivalent to .

### Example Question #44 : Algebra Ii

Simplify the following complex number expression:

Explanation:

Use the FOIL (First, Outer, Inner, Last) to multiply the complex numbers:

Combine like terms and simplify. Remember that  is equivalent to .

### Example Question #45 : Algebra Ii

Simplify the following complex number expression:

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

Combine like terms:

Simplify. Remember that  is equivalent to .

### Example Question #46 : Algebra Ii

Simplify the following complex number expression:

Explanation:

Begin by multiplying the numerator and denominator by the conjugate of the denominator:

Combine like terms:

Simplify. Remember that  is equivalent to .

### Example Question #47 : Algebra Ii

Simplify the following expression:

Explanation:

Simplifying expressions with complex numbers uses exactly the same process as simplifying expressings with one variable. In this case,  behaves similarly to any other variable. Thus, we have:

### Example Question #48 : Algebra Ii

Simplify the following complex number expression: