Recent content by dla

Homework Statement Determine the contours, C, that will follow Cauchy Integral Theorem so that \large \oint \frac{exp(\frac{1}{z^{2}})}{z^{2}+16} dz =0 Homework Equations The Attempt at a Solution The curve can't include z=±4i and z=0 but how do I come up with a curve that does...

Homework Statement Find the integral and determine whether Cauchy's Theorem applies. Use partial fractions. \large \oint \frac{tan \frac{z}{2}}{z^{4} -16} dz C the boundary of the square with vertices ±1, ±i cw Homework EquationsThe Attempt at a Solution I just wanted to check if approach is...

I got it now, thanks for your help! Much appreciate it.

I'm not quite understanding what it means when RC << T or RC >> T?

I understand the first one now. How do I go about doing the second one? When the resistor is in parallel I expected to see a the capacitor discharging/charging but my stimulation shows a rectangular waveform for the output

The voltage over the capacitor + the voltage at Vin will equal output voltage?

Impedance should be 0 at high frequency. I'm not sure if it's high or low frequency but I'm guessing step voltage is high frequency because of its sudden changes in voltage.

Homework Statement Given that the diodes are ideal for the circuits a) and b), plot each of their output for the input shown. Label the most positive and most negative levels. Assume CR >> THomework Equations The Attempt at a Solution I am having a really hard time understanding the role of...

Oh I get it now thank you so much Tsunoyukami that's a really useful method! And thanks for the explanations SteamKing I know where I went wrong now, I find that drawing it actually really helps a lot.

How did you get z(t)=(1-t, i) for i to 1-i? I don't think I have the general idea down, I thought it'd be -t for the real part since it's changing and the imaginary parameter will be constant, thus z(t)=(-t, 1+i)?

Hi SteamKing, Thanks for replying, I see what you did. I tried it for the other curves just to check if my understanding is correct, so from i to 1+i is the representation, z(t)=t+i 0≤t≤1? How did you know t is between 0≤t≤1? Also how do I take direction into account for example if it is from...

1. Homework Statement [/b] \int _{C} Re z^{2} dz clock wise around the boundary of a square that has vertices of 0, i, 1+i, 1.Homework Equations \int_{c} f(z) dz = \int \stackrel{b}{ _{a}} f[z(t)] \stackrel{\cdot}{z(t)}dtThe Attempt at a Solution Since it is piece-wise continuous I know I need...

Homework Statement Solve for z^4 +16=0Homework Equations The Attempt at a Solution What I first did was square rooted both sides to get z^2 = ±4i, but I don't how to continue from there. I'm guessing we have to find the roots from z^2=4i and then from z^2=-4i separately any help will be much...

Oh that makes a lot more sense! Very much appreciated, thanks gneill!

Thanks for the replies everyone. And I see it now CWatters thank you. Actually marcusl your reply made me wonder how did we know that n is not 1? When I made the two equations, I thought I had three unknowns at first: n, V_T and I_s. I didn't know if I should have assumed n=1 or assumed V_T...