You are here:

Algebra/Linear Algebra

Advertisement

Expert: - 9/2/2009


Question
I am trying to calculate a complex numbers problem... I need to show that ((-1+sqrt(3)i)/2)^3 is equal to 1.  I'm not quite sure how to calculate this with the i.  

Answer
Hello Kristina,

So you have ((-1+sqrt(3)i)/2)^3

The first thing you should realize is that you can write this as

(a+bi)^3

You can convince yourself of this by substituting

a=-1/2

and

b=sqrt(3)/2

right?

So all you need to do is carry out the expansion of the binomial to the power of 3.

You'll get

(a+bi)^3 = a^3 + 3(a^2)(bi) + 3a(bi)^2 +(bi)^3

Now, it's important to remember that

i^2=-1, i^3=-i, i^4=1, etc.

so you can substitute these results into the equation above. After you've done that, all you need is to plug the numbers back in (a and b) and simplify. It should work out!

Hope this helps but let me know if you still have problems with it.

Cheers,
David  

Algebra

All Answers

Answers by Expert:

Ask Experts

Volunteer

David Montiel

Expertise

PLEASE READ THIS BEFORE POSTING YOUR QUESTION: While I am glad to offer HELP with problems, I refuse to SOLVE problems. There is a difference. Please do not just copy a question from a texbook or assignment. I WILL REJECT IT. I will only accept questions if, in addition to the statement of the problem, you describe in detail what you have tried so far in order to solve it, and what exactly is the problem you are encountering. In other words where/why are you stuck? I can answer questions at the level of the first couple of undergraduate years (in science and engineering) or below. You can ask me about algebra, trigonometry, basic probability and statistics, calculus, vector calculus, differential equations and Fourier analysis. I will not answer advanced (at the graduate level) math questions. Questions in Spanish are also welcome.

Experience

Over 8 years of private tutoring in Math and Physics. Five years as a Teaching Assistant in Physics.

Education/Credentials
BSc in Chemical Engineering. MSc in Chemical Physics. PhD in Physics.

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