what is the result or simplification of
( ln(i^2) )^2
Easy as pi
Then note that exp(i pi) = -1.
So ln(-1) = ln[exp(i pi)] = i pi.
Square it: (i pi)^2 = - pi^2.
EDIT: I should caution that this is a solution. I make no claim that it is the only solution.
[itex]-\pi^2[/itex] is definitely a solution. I'm not sure how there could be more solutions...?
He wasn't even referring to solutions, was he? He just wanted a simplification of an expression, no?
Well, heh, right, not solutions... I meant that [itex]-\pi^2[/itex] is the simplest possible form for it. I see what Janitor was saying now -- that there may be better simplifications. If so, I don't see any.
Cookiemonster: he did ask, "What is the result..."
Chroot, here's the sort of thing I am worried about:
Note that exp(3 i pi) = -1.
So ln(-1) = ln[exp(3 i pi)] = 3 i pi.
Square it: (3 i pi)^2 = - 9 pi^2.
the principal branch is usually what we mean when we ask for log of a complex number, which is the same as the principal value of arg, ie Arg
thanks for all ur help dudes, and yea I believe this is a solution aswell as a simplification.
When I took complex analysis, we used ln for the multivalued version and Ln for the principal branch.
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