You are here:

Advanced Math/Evaluate i^21....

Advertisement

Expert: Sherman D. - 6/27/2005


Question
Evaluate i^21.  

Answer
i = sqrt(-1)
i^2 = -1
i^3 = i^2 * i^2 = -1 * i = -i
i^4 = i^3 * i = -i * i = -(i^2) = -(-1) = 1

Continue to do this, and you will get the pattern

i
-1
-i
1

i^21 = (i^4)(i^4)(i^4)(i^4)(i^4)(i)
i^21 = (i^4)^5 * i
i^4 = 1
so
i^21 = (1)^5 * i = 1 * i = i

This only works because i^4 is the last of the pattern.

For further help, you can go to www.quickmath.com, click on Solve under Equations, then type in x = (sqrt(-1))^21, and it will let you know that x = i

Advanced Math

All Answers

Answers by Expert:

Ask Experts

Volunteer

Sherman D.

Expertise

I can answer questions dealing in mathematics of all kinds except for Physics and Calculus, but i can answer questions in Pre-Calculus and Chemistry. I can also answer questions in Recipes of all kinds. I can find games cheats/walkthroughs, but i can`t find a specific game online or offline. I can also do history and recipes for alcoholic beverages.

Experience

Mathematics, Recipes, History, and Games.

Education/Credentials
High School graduated. I graduated with honors, and i was in Beta Club for a year and a half.

Awards and Honors
Principle's list and A and B honor roll in high school only.

©2012 About.com, a part of The New York Times Company. All rights reserved.