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Find the three cubes roots of -27 and illustrate them using an Argand diagram.
Thank You.

2007-03-14 02:04:18 · 3 answers · asked by Anonymous in Science & Mathematics Mathematics

3 answers

Not sure about the Argand diagram. You want to represent -27 as a complex number -27 + 0i. Then the first cube root would be -3, and the other two have magnitude 3. The angles made with the real axis are 60 degrees and -60 degrees (pi/3 radians and -pi/3 radians) so you get 3*e^(i*pi/3) and 3*e^(-i*pi/3). Use Euler's identity to simplify: 3*e^(i*pi/3) = 3 ( cos pi/3 + i sin pi/3) = 3 (1/2 + i*sqrt(3)/2) = (3 + 3*sqrt(3) i)/2. The other number is (3 - 3*sqrt(3) i)/2.

2007-03-14 02:18:23 · answer #1 · answered by Ken M 3 · 1 0

I'm not sure. But only some people will help you, people keep giving me **** when I ask for help. So be prepared for some people to tell you to do your own homework, if I knew the answer i'd tell you though.

2007-03-14 02:10:26 · answer #2 · answered by hev_1985 4 · 0 0

I hope you´ll appreciate. I draw it specially for you. Just click on the link

http://www.ouviringles.com/files/argand_diagram_root3_-27.JPG

2007-03-14 02:46:37 · answer #3 · answered by diamond 3 · 0 1

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