### All SAT Math Resources

## Example Questions

### Example Question #41 : Complex Numbers

Raise to the fourth power.

**Possible Answers:**

None of these

**Correct answer:**

The easiest way to find is to note that

.

Therefore, we can find the fourth power of by squaring , then squaring the result.

Using the binomial square pattern to square :

Applying the Power of a Product Property:

Since by definition:

Square this using the same steps:

Therefore,

### Example Question #42 : Complex Numbers

Raise to the third power.

**Possible Answers:**

None of these

**Correct answer:**

To raise any expression to the third power, use the pattern

Setting :

Taking advantage of the Power of a Product Rule:

Since and :

Collecting real and imaginary terms:

### Example Question #51 : Squaring / Square Roots / Radicals

Evaluate:

**Possible Answers:**

The expression is undefined

**Correct answer:**

is defined to be equal to for any real or imaginary and for any real ; therefore,

To evaluate a positive power of , divide the power by 4 and note the *remainder*:

Therefore,

Substituting,

Rationalizing the denominator by multiplying both numerator and denominator by :

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