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2bornot2b
Group Title
Can someone explain why the last equality is possible?
\[\large{a^b=(re^{i\theta })^b}\]\[\large{=(e^{ln~r+i\theta})^b=e^{(ln~r+i\theta)b}} \]
 2 years ago
 2 years ago
2bornot2b Group Title
Can someone explain why the last equality is possible? \[\large{a^b=(re^{i\theta })^b}\]\[\large{=(e^{ln~r+i\theta})^b=e^{(ln~r+i\theta)b}} \]
 2 years ago
 2 years ago

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shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
@2bornot2b , \[\huge r = e^{\ln(r)}\] Using this the result is got
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
As far as I know \(\large(e^z)^w\ne e^{zw}\) rather \(\large(e^z)^w=e^{(z+2n\pi i)w} \)
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
@shivam_bhalla I am talking about the equality that appears next to the one you have talked about.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
@2bornot2b .OK. I got what you are asking for. Let me research on this and get back to you. Looks like you are doing some extensive research on complex numbers @2bornot2b
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
Thanks @shivam_bhalla I need this help extensively.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
I think b is complex number , right ??
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
By the way, the result that I typed in my question is from the link http://en.wikipedia.org/wiki/Exponential_function#Computation_of_ab_where_both_a_and_b_are_complex
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
I believe so, but it would be better for you to check it at that link
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
@2bornot2b , I suggest you read it again properly. It says in the case you have taken that b is integer. Read this last statement "However, when b is not an integer, this function is multivalued, because θ is not unique (see failure of power and logarithm identities)."
 2 years ago

SmoothMath Group TitleBest ResponseYou've already chosen the best response.0
Um... isn't it just exponent rules? (a^b)^c = a^(b*c)
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
Here:http://en.wikipedia.org/wiki/Exponential_function#Computation_of_ab_where_both_a_and_b_are_complex
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
Sounds reasonable @shivam_bhalla But the topic starts with the name Computation of \(a^b\) where both a and b are complex
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
The way the article is written is very confusing. They should have clearly spacified that b is integer in this case and "a" is a complex number in consideration
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
*specified
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
Seems to me you are right, otherwise that line wouldn't have been mentioned at the end. What do others think?
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
@Mertsj What do you think? @shivam_bhalla how about editing the page, and refining it for future readers?
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
@2bornot2b , good idea. I think you should go ahead :)
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
Anyway thanks a lot, that really helped me a lot.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
@2bornot2b , a serious bug at OS. See the attachment See your name is replaced by "Best answer"
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
@cshalvey, check a serious bug above ^^
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
Great catch Shivam!
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
By the way shivam, can you suggest me a good book on complex functions?
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
And I think Officer @shadowfiend is in the department of arresting bugs.
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
Seriously, I didn't refer any book for complex numbers. I just listened to what my teacher taught in my class. That's it :D. If you are looking for some books, here is a book recommended by my friend HIGHER ALGEBRA By Hall & Knight
 2 years ago

2bornot2b Group TitleBest ResponseYou've already chosen the best response.1
Does that book have complex functions?
 2 years ago

shivam_bhalla Group TitleBest ResponseYou've already chosen the best response.2
I am not sure. If I remember correctly, this is the book he mentioned. Have a look at the ebook here http://books.google.co.in/books?id=wkmvDIFfJAgC&pg=PA432&dq=HIGHER+ALGEBRA+By+Hall+%26amp;+Knight++complex+numbers&hl=en&sa=X&ei=sUlT8uhEITIrQeKw_3vAQ&ved=0CD8Q6AEwAA#v=onepage&q&f=false
 2 years ago
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