If "a" be a non zero complex number and z be any complex number then define a^z.
Also what is the principal value of a^z If "a" be a non zero complex number and z be any complex number then define a^z.
Also what is the principal value of a^z @Mathematics

Question

perl · Answer

take the log of of this

anonymous · Answer

I know how to take the log and then solve it. But I don't understand, what they mean by defintion

perl · Answer

what are in your notes

anonymous · Answer

Its a question in our examination from past years

anonymous · Answer

and it says "If "a" be a non zero complex number and z be any complex number then define a^z."

anonymous · Answer

I really don't undersand how to define this..

anonymous · Answer

What do you think?

perl · Answer

here http://en.wikipedia.org/wiki/Exponentiation#Powers_of_complex_numbers

anonymous · Answer

But these are complex number..

perl · Answer

yes, it says complex

perl · Answer

For complex numbers a and b with a ≠ 0, the notation ab is ambiguous in the same sense that log a is.

To obtain a value of ab, first choose a logarithm of a; call it log a. Such a choice may be the principal value Log a (the default, if no other specification is given), or perhaps a value given by some other branch of log z fixed in advance. Then, using the complex exponential function one defines

perl · Answer

a^b*

perl · Answer

so we have a^b = e^ ( ln (a^b)) = e^ ( b ln a )

anonymous · Answer

So in one word, we can say the definition of a^b=e^ ( b ln a )

anonymous · Answer

is that so?

perl · Answer

taking the principal value of ln a

anonymous · Answer

Ok, so the problem is solved is solved, I suppose, isn't it?

perl · Answer

and be careful when you read this, Log z is a special function

perl · Answer

it is not log base 10 , lol

anonymous · Answer

I know, its ln, right?

perl · Answer

err, im wrong , i dont really kno

perl · Answer

hey, do you have a pdf or website on complex math?

perl · Answer

log is base ten generally

anonymous · Answer

I am not getting you, what I meant to say, is the log to the base e is called ln

perl · Answer

oh yes

perl · Answer

where is your pdf on complex math!

perl · Answer

or your class has some online reading i bet

perl · Answer

quick before i fall asleep

anonymous · Answer

I don't have any pdf, I follow books, recommended to me by my profs

anonymous · Answer

Ok thank you so much for the help. Hope you will help me again in future. Is there a way by which I can direct you to my questions?