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Example Questions
Example Question #268 : Exponents
Solve for .
Possible Answers:
Correct answer:
Explanation:
If we combine into a single logarithmic function we get:
Solving for we get .
Example Question #262 : 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.
i1 = 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.
Yongmao
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