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Math Help - Complex Numbers of Modulus 1

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    Junior Member universalsandbox's Avatar
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    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.
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    Quote Originally Posted by universalsandbox View Post
    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.
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