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

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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.**