SOLUTION: I need help with this problem. (-16)^1/4. Thank you very much for your help. I am very confused with this problem. I appreciate the help I get and thank you very much for your

Algebra ->  Radicals -> SOLUTION: I need help with this problem. (-16)^1/4. Thank you very much for your help. I am very confused with this problem. I appreciate the help I get and thank you very much for your       Log On


   

Question 360443: I need help with this problem. (-16)^1/4. Thank you very much for your help. I am very confused with this problem. I appreciate the help I get and thank you very much for your help. Thanks very much!
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
%28-16%29%5E%281%2F4%29+=+sqrt%28sqrt%28-16%29%29+=+sqrt%284i%29+=+2sqrt%28i%29. We have to evaluate sqrt%28i%29. We have to find real numbers a and b such that
%28a%2Bib%29%5E2+=+i. Expanding,
a%5E2-b%5E2%2B2abi+=+i, or
a%5E2-b%5E2+=+0, and 2ab+=+1.
a%5E2=b%5E2 and 4a%5E2b%5E2+=+1. After substitution,
4a%5E4+=+1. This gives a+=+1%2Fsqrt%282%29or a+=+-1%2Fsqrt%282%29. the answer won't satisfy%28a%2Bib%29%5E2+=+i, so a+=+1%2Fsqrt%282%29. Therefore
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