# Complex Functions Homework: Find Limit

• m_s_a

## 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

result

## The Attempt at a Solution

Last Qiustion: http://www.a7bk-a-up.com/pic/Nww95795.bmp

## 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

result

## The Attempt at a Solution

cos(pi/2)+i*sin(pi/2)=i, not i^(1/2). ?

Last Qiustion: http://www.a7bk-a-up.com/pic/Nww95795.bmp

But what? Isn't the limit still 1?

cos(pi/2)+i*sin(pi/2)=i, not i^(1/2). ?

By imposing
I said let w=i===>w^2=-1

But what? Isn't the limit still 1?

Yes,
Find this limit

By imposing
I said let w=i===>w^2=-1

I don't understand that at all.

Yes,
Find this limit

Substitute zbar for z in the power series. What's wrong with that?

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.

Like this
http://www.a7bk-a-up.com/pic/ydi48834.bmp

Infact:
http://www.a7bk-a-up.com/pic/LpB47687.jpg
delta=?

Sure. |(sin(z*)/z*|=|sin(z)/z|. Because (sin(z)/z)*=(sin(z*)/z*) and |z|=|z*|. So you don't need analyticity, correct?

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 very much In Arabic: شكرًا جزيلاً

Sure. Sorry, I'm not good at the script. afwan.

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

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. :)

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