Find all values complex equation

alexcc17
Messages
48
Reaction score
0

Homework Statement


i.5 - i


Homework Equations


zc=ec log(z)

z1/n=exp[(1/n) log(z)], n is in integer


The Attempt at a Solution



letting c=.5-i and z=i so

zc=e(.5-i) log(i) = e.5 log(i)*e-i log(i)

from the second equation I reduced it to:
i.5*e-i log(i) but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part
 
Physics news on Phys.org
alexcc17 said:

Homework Statement


i.5 - i


Homework Equations


zc=ec log(z)

z1/n=exp[(1/n) log(z)], n is in integer


The Attempt at a Solution



letting c=.5-i and z=i so

zc=e(.5-i) log(i) = e.5 log(i)*e-i log(i)

from the second equation I reduced it to:
i.5*e-i log(i) but I'm not sure where to go from there since the second known equation doesn't apply to the e^(-i log(i)) part

exp(log(i)*(.5-i)) is a good start. Now figure out what possible values log(i) could have.
 
I got it thanks though
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top