Finding the Value of z and its Derivatives

  • Thread starter Thread starter uniidiot
  • Start date Start date
  • Tags Tags
    Derivatives Value
AI Thread Summary
The discussion revolves around finding the value of z and its derivatives, specifically for z = 3 + 2i. The term "z with a horizontal line above it" refers to the complex conjugate, denoted as \overline{z}, which is calculated as x - iy when z = x + iy. Participants clarify that the horizontal bar indicates the complex conjugate, which is essential in complex number calculations. The conversation highlights the importance of understanding complex conjugates in mathematical contexts. Overall, the exchange emphasizes the utility of recognizing and using the complex conjugate in calculations involving complex numbers.
uniidiot
Messages
24
Reaction score
0
this will probably seem like a really stupid question but here goes.

If z = 3 + 2i find the following

i) z

ii) z x z(with a horizontal line above it)

iii) z^2

what does the horizontal bar mean, i can't find it in my reivsion books lol.

Thanks
 
Physics news on Phys.org
I suspect that a) was \overline{z} rather than just z itself!

\overline{z} is the "complex conjugate", a remarkably useful form: if z= x+ iy then \overline{z}= x- iy.
 
thankyou!

and yes a) was suposed to be \overline{z} lol
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top