All PSAT Math Resources
Example Questions
Example Question #17 : How To Find Patterns In Exponents
Solve for .
Possible Answers:
Correct answer:
Explanation:
If we combine into a single logarithmic function we get:
Solving for we get .
Example Question #261 : 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.
Lorie
Certified Tutor
Certified Tutor
Appalachian State University, Doctorate (PhD), Educational Leadership - Instructional Tech.
All PSAT Math Resources
Popular Subjects
Algebra Tutors in San Francisco-Bay Area, Computer Science Tutors in Philadelphia, GMAT Tutors in Chicago, Chemistry Tutors in Atlanta, Calculus Tutors in San Diego, Computer Science Tutors in Denver, Physics Tutors in Washington DC, SSAT Tutors in Chicago, Statistics Tutors in New York City, English Tutors in Philadelphia
Popular Courses & Classes
SAT Courses & Classes in Philadelphia, Spanish Courses & Classes in Chicago, Spanish Courses & Classes in Boston, LSAT Courses & Classes in Houston, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in San Diego, ACT Courses & Classes in Washington DC, Spanish Courses & Classes in Miami, GRE Courses & Classes in San Francisco-Bay Area, GRE Courses & Classes in Seattle
Popular Test Prep
MCAT Test Prep in Seattle, SSAT Test Prep in Denver, ISEE Test Prep in Chicago, SAT Test Prep in Washington DC, GRE Test Prep in Washington DC, MCAT Test Prep in Boston, SSAT Test Prep in Philadelphia, SAT Test Prep in Chicago, ACT Test Prep in Washington DC, LSAT Test Prep in Dallas Fort Worth