Can you Solve this? | Math Olympiad

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Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
Can You Solve For 'n'? | Math Olympiad Questions | A Beautiful Exponential Problem | Algebra problem
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#exponentialproblems #matholympiad #maths

[Grecks]

What you've shown is not accurate mathematically. Complex exponentiation is defined by means of the complex exponential and complex log functions as z^w = exp(w*ln(z)). If you want to define complex exponentiation as a single-valued function you have to decide upon a specific branch of the complex log function. The usual definition takes the principal value of the complex log function, i.e. Log(z) with an imaginary part in the interval (-pi, pi].

With that definition 1^w = exp(w*ln(1)) where ln(1) is always 0 (because v=0 is the only complex number with Im(v) in (-pi, pi] that gives exp(v)=1). Therefore, we have 1^w = exp(w*ln(1)) = exp(w*0) = exp(0) = 1 for all complex numbers w. Thus, there is no complex number w with 1^w = -2, that equation simply has no solution (with the usual definition of complex exponentiation).

[blitzag]

ln is a function, which doesnt have negative numbers in its domain

[approciated]

X = N - ilog(2) / 2Nn n =/ 0 n is Z
N is pie i see the answer in wolfram why is this different?

[matthewmaas]

1 raised to any complex number is 1. The problem has no solution.

[DrBenway]

If you are going to find the Complex valued solutions to this equation, shouldn't you be writing ln(-2) as a Complex number also? The answer is yes, because ln(-2) is undefined as far as Real numbers are concerned. ln(-2) = ln(2) + ((4k - 1) * (PI) * i ) / 2 , k=1, 2, 3, 4...
Math Olympiad??? I don't think so... More like Intro To Complex variables class...

[programmingpillars]

when we put imaginary number in the power of a number just gives weird things