Complex numbers?

Question

If z1 = 1 - 5i and z2 = 3 + 4i

z1 / lz2l

i.e. What is z1 divided by (the absolute value of z2)??

Answer 1

actually, its not an absolute value :D. its called modulus. to get the modulus of say a complex number a+bi,
|a+bi|=sqrt(a^2 + b^2). Doing so for z2, |z2|=sqrt(9+16) = sqrt of 25 which is simply 5. hence, we can now divide z1 by 5:
this yields to:
z1/5 = (1-5i)/5 = 1/5 - i. there you go! i hope you understand :D:D:D

Answer 2

|z2| = √(3^2 + 4^2) = 5.
So z1 / |z2| = 1/5 - i.