I need to calculate |z| when z = 1-i / 2i

The answer is √2/2 but im having trouble getting it there... im thinking it should be 1 since the absolute value of 1-i is and 2i = 2 aswell to 2/2 = 1.. but im obviosly forgetting something here...

edit; omfg am I this stupid? √1^2+1^2= √2
and √2^2 = 2

so √2/2

This post was edited by bomben on Oct 22 2013 12:18pm

|z| isnt the absolute value of z, its the module of z

if you have z = a+bi, then |z| = sqrt(a^2 + b^2)

See it this way : a complex number is like a set of coordinates, so 1 - i would be (1,-1) where -1 is the coefficient of the imaginary part
and your module is the distance from (0,0) to (1,-1)

when you have z= 1-i/2i you do

(1-i)/2i = (1-i)/2i * -2i/-2i (multiply by conjugate to remove imaginary part from the denumerator) = (1-i)(-2i)/(-2i*-2i) = (-2i -2 )/(-4) = 1/2 + i/2

and your module (or |z|) = sqrt(1/2)^2 + (1/2)^2) = sqrt(2/4) = sqrt(2)/2

or an easier way :

|z| = |1-i|/|-2i| = sqrt(1^2 + 1^2)/sqrt(2^2) = sqrt(2)/2


nvm you figured it out

This post was edited by LeB on Oct 22 2013 07:01pm

thanks man really nice explained aswell