Name: Anonymous 2009-04-21 12:54
expand
(2-root3i)^6
The anser is supposed to be 512i
Have tried this both by binomial expansion and using De Moivres theorem, but neither method cancels out the real parts of the expression as would be neccesary to obtain a purely imaginary solution. Any ideas guise?
I might just be screwing up the binomial expansion at some point...
This is the first line of the expansion as I have it
2^6+[6.2^5.-rt3i]+[15.2^4.(-rt3i)^2]+[20.2^3.(-rt3i)^3]+[15.2^2]+[6.2.(-rt3i)^5]+(rt3i)^6
I reduced this to:
64-192rt3i-720+480rt3i+540-108rt3i-27.
But that cancels down to 180rt3i - 143.
What am I doing wrong?
(2-root3i)^6
The anser is supposed to be 512i
Have tried this both by binomial expansion and using De Moivres theorem, but neither method cancels out the real parts of the expression as would be neccesary to obtain a purely imaginary solution. Any ideas guise?
I might just be screwing up the binomial expansion at some point...
This is the first line of the expansion as I have it
2^6+[6.2^5.-rt3i]+[15.2^4.(-rt3i)^2]+[20.2^3.(-rt3i)^3]+[15.2^2]+[6.2.(-rt3i)^5]+(rt3i)^6
I reduced this to:
64-192rt3i-720+480rt3i+540-108rt3i-27.
But that cancels down to 180rt3i - 143.
What am I doing wrong?