Recent content by struggles

so modulus of 1 and argument of pi?

ah is it -1? in that case you'd have ½(-1-1) = -1. so it would just have radius of -1 modulus of π?

Homework Statement So I'm trying to find the modulus and argument of cosh(iπ) Homework EquationsThe Attempt at a Solution so far coshπi = ½(eiπ+e-iπ) I am now a bit stuck as what to do as i have two terms in the form eix and I'm not sure homework to combine them to get the argument?

so i = √-1 so i2 = -1. so 1/i must equal 1/(-1)1/2 = (-1)-1/2? is that what you were getting at fresh-_42? So axmls 1/i = i/i^2 = -i! Thanks both of you!

i-1?

Homework Statement So this is a really simple problem and i know I'm missing something really obvious but i just can't spot it. Homework EquationsThe Attempt at a Solution so in the second part above I get : e-x - ex/2i. However I don't get the next bit as the 2i on the denominator is...

So the limits would be t is from 0 to t and x from R to x which gives √R2/g2(π/2 - arcsin(x/r)) = t. Rearranging sin(π/2 - t√(g2/R2)) = cos(t√(g2/R2) = x! Thank you! think I've finally got there!

so eventually after making substitutions i get √r/√g ∫ du/√(1-u2) = √r/√g arcsin(x/r) (where u = x/r) and rearranging get x = Rsin(t√g/√R). However the next part of the question ( and that at t=0 c should = r) implies that it should be cos. Any ideas or have i just made a slip with signs...

Ok i still can't get this to work out: so after integrating i get -gm/R(x2/2 -R2/2) = mv2/2 Rearranging i get v = √(gR - gx2/R) = dx/dt Then rearranging to integrate again - dx(gR - gx2/R)-1/2 = 1dt and integrating R/gx (gR - gx2/R)1/2 This isn't right but I've played around and can't get it...

Homework Statement The question is pretty long and wordy so apologies in advance! Inside the Earth the gravitational field falls off linearly as one approaches the centre. An accurate description of motion in a very deep hole would therefore be to use Newton’s law, f = ma, but with the force...

I think that kind of makes sense. So you can view the relative change in velocity as being greater than c but it doesn't actually go faster than c? Any chance of a hint of how to do the second part of my question?

Thank you!

Oops 3π/2?

I was thinking it contains no term with i. But would ½(e-1 + e) be equal to the modulus and have an argument of o?

Homework Statement Find the modulus and argument of 1) cos(i) 2) -3i Homework EquationsThe Attempt at a Solution 1) So for question 1 i tried cos(i) = ½(ei2 + e-i2) = ½(e-1 + e) . However this doesn't (as far as I can see!) lead me to the right answer. I was aiming to get it in the form...