find all solution of Z^3/2=(1/2-i).

Results 1 to 6 of 6

- Jun 8th 2010, 09:38 PM #1

- Joined
- Dec 2008
- Posts
- 58

- Jun 8th 2010, 09:41 PM #2

- Jun 8th 2010, 09:54 PM #3

- Joined
- Dec 2008
- Posts
- 58

- Jun 8th 2010, 10:18 PM #4

- Joined
- Mar 2010
- Posts
- 715
- Thanks
- 2

- Jun 8th 2010, 10:53 PM #5
Actually it's

$\displaystyle \left(\frac{1}{2} - i\right)^{\frac{2}{3}}$.

And this is only one solution. There will be two others.

Convert to polars, use DeMoivre's Theorem to simplify, then recall that the three roots are evenly spaced around a circle to find the other two.

- Jun 9th 2010, 05:45 AM #6

- Joined
- Mar 2010
- Posts
- 715
- Thanks
- 2