Complex Numbers: Eigenvalues and Roots

[Canadian]

[SOLVED] Complex Numbers: Eigenvalues and Roots

Below are some problems I am having trouble with, the computer is telling me my answers are wrong. It may be the way I am inputting the numbers but as my final is in a week and a half I would like to be sure.

Thanks,

 

[Avodyne]

All your answers look correct to me.

To compute (-81)^(1/4), can you write -81 in polar form? Then use the same method you used on the last problem.

 

[dynamicsolo]

I'm also getting (lambda)^3 = 0 for the characteristic equation on that first matrix. Since there are supposed to be three eigenvalues, could the computer want you to input three zeroes?

On the second one, you want to apply deMoivre's Theorem, as you did on the last problem, after writing -81 in polar form. There will be four complex roots (none of them real). [I can just barely read that, BTW: is that -81^(1/4) or -81^(3/4)?]

Your solution for the last problem looks to be correct. Does the computer accept expressions like 2^(1/3) cos (pi/9) as a part of a complex number or do you need to get out a calculator and find decimal approximations for the parts?

I'll have to get back to you shortly on the second eigenvalue problem.

 

[dynamicsolo]

Your answer to the third problem looks OK to me, too. Again, will the computer take sqrt(5) as an entry or do you need to give it 2.236? Make sure you are entering all your complex number results as two parts. You may need to check with someone as to what the acceptable form for complex number entry is.

 

[Canadian]

Thanks for the help, the two eigenvalue questions were accepted after putting the answer in decimal form.

I'm headed off to bed now, will try the rest tomorrow morning.