You are here:

Calculus/DeMoivre's theorem

Advertisement

Expert: - 12/3/2008


Question
I need to use DeMoivre's theorem to find what (1-i)^3 is, using rectangular coordinates.
I know it needs to be rewritten. I've looked through my book and can't seem to get past the second step.
Thanks very much for your help.  

Answer
DeMoivre's theorem is a way to convert from polar to rectangular coordinates.  When a number in polar coordinates is cubed, the angle is multiplied by 3 and the length is cubed.

The length of the number is √2 of the number cubed is 2√2.  The angle is -45°, so the angle of the answer is -135°, which is the same as 360-135=225°, or 45° down in the bottom left quadrant.

To convert that to polar coordinates, note that the magnitude of x and y must be the same since it is at 45°.  The x and y values must be negative, though.  We also know that x²+y²=(2√2)²=8, so x and y must both have magnitude 4.  Since they are in the lower left quadrant, x and y both need to be negative.

They are both negative with magnitude 4, so it looks like they are both -4.

Calculus

All Answers

Answers by Expert:

Ask Experts

Volunteer

Scotto

Expertise

Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

Experience

Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

Publications
Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

Education/Credentials
I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

Awards and Honors
I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

Past/Present Clients
My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

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