Find the argument and the absolute value of the complex number z = 2 + i*3^1/2/2

The absolute value of a complex number is also called the
modulus of the complex number and it can be found from rectangular
form:

z = x + i*y (rectangular
form)

Modulus: |z| = sqrt(x^2 +
y^2)

We'll identify the real part and the imaginary part of
z:

x = Re(z) = 2

y = Im(z) =
(sqrt 3)/2

Now, we'll calculate the
modulus:

|z| = sqrt[2^2 +
(sqrt3)^2/4]

|z| = sqrt
(4+3/4)

|z| = sqrt
(19/4)

|z| = sqrt
(19)/2

The modulus of the
given complex number is |z| = sqrt
(19)/2.

The argument of the complex number
is the angle to x axis.

arg(z) =
a

tan a =
y/x

tan a = (sqrt
3)/4

a = arctan[(sqrt 3)/4] +
k*pi

arg(z) = arctan[(sqrt
3)/4] + k*pi