Math Is Fun Forum

magic_box

Guest

me again...complex derivative confusion

hi,

i'm a bit stuck here. i was just experimenting with complex number derivatives and i don't know what to do now.

we know that:

we can observe through calculation that:

can we extend this to complex numbers? lets try:

we haven't done any calculations for this one so we'll do this below:

simplifying:

but we know that the FIRST derivative of x is just 1, so:

but this implies that:

so where to go from here? how do i show that:

?

please help, i'm very stuck. thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: me again...complex derivative confusion

Hi magic_box ;

Since x is a variable, is it not. What could the denominator possibly equal that would make that expression equal  to 1. It would have to equal x, but x is a variable not a fixed constant.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

magic_box

Guest

Re: me again...complex derivative confusion

hello,

thanks for your reply..

yes, i was thinking this too...x is not a fixed constant and is a variable, so this is where i got stuck.

so, assuming that i just had

as my first derivative, is there any way to simplify this further?

i mean, i'm just trying to see how you can arrive at the first derivative of x by using;