1. Use DeMoivre's theorem to find all the indicated roots. Find the three cube roots of 3 - 4i

2. One cube root of -1 is (1/2) - (1/2)*i*square root of 3. Cube this number in rectangular form and show that the result is -1.

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- Jan 18th 2008, 04:14 PMOzzManDeMoivre's Thereom
1. Use DeMoivre's theorem to find all the indicated roots. Find the three cube roots of 3 - 4i

2. One cube root of -1 is (1/2) - (1/2)*i*square root of 3. Cube this number in rectangular form and show that the result is -1. - Jan 18th 2008, 04:55 PMPlato
The three cube roots of 3-4i are located on a circle with radius , the real cube root of the absolute value of 3-4i, at three equal arcs. So each arc is measured at . So let then one root is

What are the other two? - Jan 18th 2008, 05:09 PMOzzMan
well my teacher got 5 as the radius which i get and 306.87 degrees as the angle theta (might be mispelled). but then he goes from there to 5^(1/3)e^(306.87 degrees*i) sorry if this is cluttered. then he put that in polar form. but somewhere along the road he did the angle theta + 360/ 3 which got 222.3 degrees. from there i guess he got the other 2 roots. but im just a little confused in the methods used here. Sorry to ask but can you break it down into a step by step process, if possible? sorry i should be using latex for this stuff.

- Jan 18th 2008, 05:30 PMtopsquark