# Thread: Complex Numbers of Modulus 1

1. ## Complex Numbers of Modulus 1

Show the complex numbers of modulus 1 form a group under multiplication.

|z| = √(x^2 + y^2)

Before doing this, could someone please explain in words (and mathematical notation) what the complex numbers of modulus 1 is? Thank you.

2. Originally Posted by universalsandbox
Show the complex numbers of modulus 1 form a group under multiplication.

|z| = √(x^2 + y^2)

Before doing this, could someone please explain in words (and mathematical notation) what the complex numbers of modulus 1 is? Thank you.
A complex number $z$ is $z\in \mathbb{R}\times \mathbb{R}$. Thus, $z=(x,y)$ - we just write $x+iy$ as a notational thing. The modulos of a complex number is $|z|$ and it is defined as $\sqrt{x^2+y^2}$. Thus, if $|z| = 1$ then it means $x^2+y^2 = 1$.