What are the argument and the modulus of the complex number z=1+i*3^1/2 ?

If z = x+iy,

Then we can
write this in the polar form as r (cosp +isinp)

where  r =
sqrt(x^2+y^2).

x = rcosp

y = r
sin p.

So tan p =
y/x.

Therefore p = arctan (y/x) is called argument of
x+iy.

Also r = sqrt(x^2+y^2) is the modulus of z or
(x+iy).

Given z =
1+i*3^(1/2).

Therefore modulus of z = |z| =
sqrt{1^2+(3^1/2)^2}

|z| = sqrt(1+3) = sqrt4 =
2.

Therefore modulus of z = |z| =
2.

Argument of 1+i*3^(1/2) =  arc tan (3^1/2)/1 = arc tan
(sqrt3)= pi/3.

Therefore argument of z = argument of
(1+i*3^1/2) = pi/3 or 60 degree.