What is the modulus of complex number z if z+2z'=3+i?z' is conjugate of z

First, we'll recall the rectangular form of a complex
number z:

z = x + i*y, where x represents the real part and
y represents the imaginary part.

Since z' is the conjugate
of z, we'll write z':

z' = x -
i*y

Now, we'll re-write the expression provided using the
rectangular forms:

x + i*y + 2x - 2i*y = 3 +
i

We'll combine real parts and imaginary parts from the
left side:

3x - i*y = 3 +
i

Comparing both sides, we'll
get:

3x = 3 => x = 1

-y
= 1 => y = -1

Since we know now the real and
imaginary parts, we'll determine the modulus of z:

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

|z| =
sqrt(1+1)

|z| =
sqrt2

The requested modulus of the complex
number z is; |z| = sqrt2.