MHB Proof of Complex Numbers: Delta*w(z, z) Explained

Bat1
Messages
4
Reaction score
0
Hi,
I have this problem and its solution but i know what right size is, but i don't understand what left size (delta*w(z, z)) is equal to
IMG_20211025_180923.jpg
 
Physics news on Phys.org
? There is NO [math]\delta* w(z, Z)[/math]. If you meant [math]\delta w(z, z*)[/math] then it is the change in w when z, and its conjugate z*, change by a slight amount.
 
I know it is NOT A MULTIPLICATION, I know what "delta" means... I don't know how to prove that equation (17)
 
Write $\delta w= w(x+\delta x, y+\delta y, z+ \delta z)- w(x, y, z)$. Use the mean value theorem.
 
\[ if: w=w(x,y), and: w=u+iv, then: u==x, v==y, then, w=x+iy (??) \]
\[ \delta w=w(x+\delta x, y+\delta y) - w(x, y)=\delta x +i\delta y \]

\[ \delta z(\partial w/\partial z)+\delta z^*(\partial w/\partial z^*) =\delta (x+iy)* 0.5*(\partial w/\partial x+i*\partial w/\partial y)+\delta (x-iy)* 0.5*(\partial w/\partial x-i*\partial w/\partial y)=\delta x*(\partial w/\partial x) +\delta y*(\partial w/\partial y)=\delta x*(\partial u/\partial x+i\partial v/y) +\delta y*(\partial u/\partial y+\partial v/y)= \]\[ if: u==x, v==y, then: \]
\[ \partial u/\partial x=1,\partial v/\partial x=0,\partial u/\partial y=0,\partial '/\partial x=1, \]\[ = \delta x +i\delta y \ \]

Is this the right solution??
 
Thread 'Determine whether ##125## is a unit in ##\mathbb{Z_471}##'
This is the question, I understand the concept, in ##\mathbb{Z_n}## an element is a is a unit if and only if gcd( a,n) =1. My understanding of backwards substitution, ... i have using Euclidean algorithm, ##471 = 3⋅121 + 108## ##121 = 1⋅108 + 13## ##108 =8⋅13+4## ##13=3⋅4+1## ##4=4⋅1+0## using back-substitution, ##1=13-3⋅4## ##=(121-1⋅108)-3(108-8⋅13)## ... ##= 121-(471-3⋅121)-3⋅471+9⋅121+24⋅121-24(471-3⋅121## ##=121-471+3⋅121-3⋅471+9⋅121+24⋅121-24⋅471+72⋅121##...

Similar threads

Back
Top