Complex Functions Homework: Find Limit

In summary, the conversation discusses finding the limit of a given function and using a power series to solve for the limit. There is a disagreement about the use of analyticity in the solution, but it is ultimately resolved. The conversation also briefly touches on learning Arabic and the exchange of pleasantries.
  • #1
m_s_a
88
0

Homework Statement


Find the limit :

http://www.a7bk-a-up.com/pic/uDs93333.bmp
http://www.a7bk-a-up.com/pic/zAP94166.bmp


The Attempt at a Solution


http://www.a7bk-a-up.com/pic/g0Q93947.bmp

Homework Statement








result


The Attempt at a Solution

 
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  • #2
Last Qiustion::biggrin:
http://www.a7bk-a-up.com/pic/Nww95795.bmp
 
  • #3
please wait:zzz:
 
  • #4
m_s_a said:

Homework Statement


Find the limit :

http://www.a7bk-a-up.com/pic/uDs93333.bmp
http://www.a7bk-a-up.com/pic/zAP94166.bmp


The Attempt at a Solution


http://www.a7bk-a-up.com/pic/g0Q93947.bmp

Homework Statement








result


The Attempt at a Solution


cos(pi/2)+i*sin(pi/2)=i, not i^(1/2). ?
 
  • #5
m_s_a said:
Last Qiustion::biggrin:
http://www.a7bk-a-up.com/pic/Nww95795.bmp

But what? Isn't the limit still 1?
 
  • #6
Dick said:
cos(pi/2)+i*sin(pi/2)=i, not i^(1/2). ?

By imposing
I said let w=i===>w^2=-1
 
  • #7
Dick said:
But what? Isn't the limit still 1?

Yes,
Find this limit
 
  • #8
m_s_a said:
By imposing
I said let w=i===>w^2=-1

I don't understand that at all.
 
  • #9
m_s_a said:
Yes,
Find this limit

Substitute zbar for z in the power series. What's wrong with that?
 
  • #11
It doesn't have to be analytical. You've shown using the series (or l'Hopital) that if z_n is a series of complex numbers approaching 0, then sin(z_n)/z_n->1. z_n* is also a series of complex numbers approaching 0. The series expansion holds for ANY z.
 
  • #12
Like this
http://www.a7bk-a-up.com/pic/ydi48834.bmp
 
  • #13
Infact:
http://www.a7bk-a-up.com/pic/LpB47687.jpg
delta=?
 
  • #14
Sure. |(sin(z*)/z*|=|sin(z)/z|. Because (sin(z)/z)*=(sin(z*)/z*) and |z|=|z*|. So you don't need analyticity, correct?
 
  • #15
Dick said:
Sure. |(sin(z*)/z*|=|sin(z)/z|. Because (sin(z)/z)*=(sin(z*)/z*) and |z|=|z*|. So you don't need analyticity, correct?

Dear: Dick
correct 100%.


Thank you for answering me
Thank you very much:blushing:
In Arabic:
:biggrin:شكرًا جزيلاً
 
  • #16
Sure. Sorry, I'm not good at the script. afwan.
 
  • #17
Dick said:
Sure. Sorry, I'm not good at the script. afwan.

O. My Dod
afwan
very very Excellent
Rather than to learn English
You have learned Arabic
 
  • #18
shukran, afwan, is about as far as I go. Oh, and salam alekum. That's it. I don't even remember how to count, even though this is a math site. So you might want to keep learning english. :)
 
Last edited:
  • #19
show that :
 

What is a complex function?

A complex function is a mathematical function that operates on complex numbers, which are numbers that can be written in the form a + bi, where a and b are real numbers and i is the imaginary unit, equal to the square root of -1.

What is a limit of a complex function?

A limit of a complex function is the value that the function approaches as the input approaches a specific value. It is a fundamental concept in calculus and is used to analyze the behavior of functions at certain points.

How do I find the limit of a complex function?

The limit of a complex function can be found by evaluating the function at points close to the specified input value and observing the pattern of the output values. If the function approaches a specific value as the input gets closer and closer, that value is the limit. This can also be done algebraically using limit laws and techniques such as L'Hopital's rule.

Why is finding limits of complex functions important?

Finding limits of complex functions is important because it allows us to understand the behavior of the function at specific points and to analyze its properties, such as continuity and differentiability. It also has practical applications in fields such as physics and engineering.

What are some common strategies for finding limits of complex functions?

Some common strategies for finding limits of complex functions include using algebraic techniques such as factoring and rationalizing, using limit laws such as the sum, difference, and product rules, and using special techniques such as L'Hopital's rule. Graphing the function or using a table of values can also help in determining the limit of a complex function.

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