Question

find |z| and Arg (z) if Z=1-i.​

Answer 1

z = 1-i

|z| = √(1²+(-1)²)

=>√1+1 = √2

So,

|z| = √2

Now,

tan x = |Im(z)/Re(z)| = |-1/1| = 1

so, x = 45° that is π/4

Now, z represented in points is (1,-1) which lies in fourth quadrant so,

Arg(z) = -x = -π/4

Cheers!