complex inputs function

ltn

New member
Joined
Oct 6, 2021
Messages
2
Hello!
I've encountered problem:
01.png
and best I came up with is:
t = 3 + ih
-ih = -t + 3
ih = t - 3
2 + 4(t-3)
4t - 10
f'(3) = 4???

I suppose, this shouldn't be solved that way, so my question is: how can this type of problem be solved?

Thank you in advance!
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
11,130
Let's see: 3 = 3+ih if h=0.
So f( 3) = f( 3+i*0) =....
 

LCKurtz

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May 3, 2019
Messages
438
Is [imath]h[/imath] real? If [imath]f[/imath] is a real valued function, how can [math]f(3+2ih) = 2+ 4ih[/math]?
 
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Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
12,598
I searched for the problem to see if it has any context that would explain the idea of a real-valued function (for real inputs?) that can also have complex inputs and outputs; the problem is found here, which appears to be rather specialized (though I couldn't find the explanation I hoped to find):


My best guess is that you are expected to use the limit definition of the derivative, and hope it will be meaningful.
 

ltn

New member
Joined
Oct 6, 2021
Messages
2
Hello!
Turns out this problem could be solved using this equation (link for reference)
1634046855126.png
So, eventually:

[imath]f'(x)=\frac{lm(2+4ih)}{h}= 4h/h = 4[/imath]
 
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