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.
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 $\displaystyle z$ is $\displaystyle z\in \mathbb{R}\times \mathbb{R}$. Thus, $\displaystyle z=(x,y)$ - we just write $\displaystyle x+iy$ as a notational thing. The modulos of a complex number is $\displaystyle |z|$ and it is defined as $\displaystyle \sqrt{x^2+y^2}$. Thus, if $\displaystyle |z| = 1$ then it means $\displaystyle x^2+y^2 = 1$.