# PSAT Math : Pattern Behaviors in Exponents

## Example Questions

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### Example Question #267 : Exponents

Solve for .

Possible Answers:

Correct answer:

Explanation:

If we combine into a single logarithmic function we get:

Solving for  we get .

### Example Question #12 : How To Find Patterns In Exponents

If  is the complex number such that , evaluate the following expression:

Possible Answers:

Correct answer:

Explanation:

The powers of i form a sequence that repeats every four terms.

i= i

i2 = -1

i3 = -i

i4 = 1

i5 = i

Thus:

i25 = i

i23 = -i

i21 = i

i19= -i

Now we can evalulate the expression.

i25 - i23 + i21 - i19 + i17..... + i

= i + (-1)(-i) + i + (-1)(i) ..... + i

= i + i + i + i + ..... + i

Each term reduces to +i. Since there are 13 terms in the expression, the final result is 13i.

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