2bornot2b
  • 2bornot2b
Can someone explain why the last equality is possible? \[\large{a^b=(re^{i\theta })^b}\]\[\large{=(e^{ln~r+i\theta})^b=e^{(ln~r+i\theta)b}} \]
Mathematics
schrodinger
  • schrodinger
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
@2bornot2b , \[\huge r = e^{\ln(r)}\] Using this the result is got
2bornot2b
  • 2bornot2b
As far as I know \(\large(e^z)^w\ne e^{zw}\) rather \(\large(e^z)^w=e^{(z+2n\pi i)w} \)
2bornot2b
  • 2bornot2b
@shivam_bhalla I am talking about the equality that appears next to the one you have talked about.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
@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
2bornot2b
  • 2bornot2b
Thanks @shivam_bhalla I need this help extensively.
anonymous
  • anonymous
I think b is complex number , right ??
2bornot2b
  • 2bornot2b
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
2bornot2b
  • 2bornot2b
I believe so, but it would be better for you to check it at that link
anonymous
  • anonymous
@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)."
anonymous
  • anonymous
Um... isn't it just exponent rules? (a^b)^c = a^(b*c)
anonymous
  • anonymous
Here:http://en.wikipedia.org/wiki/Exponential_function#Computation_of_ab_where_both_a_and_b_are_complex
2bornot2b
  • 2bornot2b
Sounds reasonable @shivam_bhalla But the topic starts with the name Computation of \(a^b\) where both a and b are complex
anonymous
  • anonymous
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
anonymous
  • anonymous
*specified
2bornot2b
  • 2bornot2b
Seems to me you are right, otherwise that line wouldn't have been mentioned at the end. What do others think?
2bornot2b
  • 2bornot2b
@Mertsj What do you think? @shivam_bhalla how about editing the page, and refining it for future readers?
anonymous
  • anonymous
@2bornot2b , good idea. I think you should go ahead :)
2bornot2b
  • 2bornot2b
:)
2bornot2b
  • 2bornot2b
Anyway thanks a lot, that really helped me a lot.
anonymous
  • anonymous
@2bornot2b , a serious bug at OS. See the attachment See your name is replaced by "Best answer"
anonymous
  • anonymous
@cshalvey, check a serious bug above ^^
2bornot2b
  • 2bornot2b
Great catch Shivam!
2bornot2b
  • 2bornot2b
By the way shivam, can you suggest me a good book on complex functions?
2bornot2b
  • 2bornot2b
And I think Officer @shadowfiend is in the department of arresting bugs.
anonymous
  • anonymous
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
2bornot2b
  • 2bornot2b
Does that book have complex functions?
anonymous
  • anonymous
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=sU-lT8uhEITIrQeKw_3vAQ&ved=0CD8Q6AEwAA#v=onepage&q&f=false

Looking for something else?

Not the answer you are looking for? Search for more explanations.