/sci/ - Science & Math

[Anonymous No.4307173]

hey mathbros.

so i'm learnding about complex functions and there's this example to introduce me to poles and branches,

f(z) = (z^2 - 1)^1/2

now, this bro defines z - 1 = r1exp(i@1), z + 1 = r2exp(i@2). for some z these are just the complex numbers from from 1 and -1 respectively.

then he says, if we encircle 1, exp(i@1/2) is 2-valued, but exp(i@2/2) is 1-valued.

i don't really get what is happening here, there are two answers for both of the square roots as far as i can tell..? what's he trying to say?

[Anonymous No.4307231]

oh come on

[Anonymous No.4307319]

>>4307231
rewrite the text in a readable way, it's terrible sorry

[Anonymous No.4307421]

>>4307319

it's really not complicated, there are just subscripts on the variables,

r1, r2, @1, @2.

apart from that i'm not sure what else you can't read.