Find the argument of the complex number.

[david102]

Homework Statement

If modulus of z=x+ iy(a complex number) is 1 I.e |z|=1 then find the argument of z/(1+z)^2

Homework Equations

argument of z = tan inverse (y/x) where z=x+iy modulus of z is |z|=root(x^2+y^2)

The Attempt at a Solution

z/(1+2z+z^2) = x+iy / 1+2(x+iy)+( x+iy)2 ...

 

[Ray Vickson]

Homework Statement

If modulus of z=x+ iy(a complex number) is 1 I.e |z|=1 then find the argument of z/(1+z)^2

Homework Equations

argument of z = tan inverse (y/x) where z=x+iy modulus of z is |z|=root(x^2+y^2)

The Attempt at a Solution

z/(1+2z+z^2) = x+iy / 1+2(x+iy)+( x+iy)2 ...

This is not correct; you have written
$$z/(1+2z+z^2) = x + \frac{iy}{1} + 2(x+iy) + (x+iy)2 $$
Did you mean
$$\frac{x + iy}{1 + 2(x+iy) + (x+iy)^2}? $$
If so, use parentheses, like this: (x + iy)/( x + iy + 2(x+iy) + (x+iy)^2). In fact, you need to also expand out (x+iy)^2 to find its real and imaginary parts. Then you need to keep going to find the real and imaginary parts of the entire expression. It will be messy and long, but that's just how it goes sometimes.

Actually, there is another approach that leads to an answer in a couple of lines of simple algebra, but PF rules forbid me from spelling it out.