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2008-05-18T19:16:42Z

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Vipul: New page: ==Definition== The '''modulus map''', denoted $| \cdot |$ , is a map $\mathbb{C} \to [0,\infty)$ , denoted by: $z \mapsto |z|$ It is defined as follows. I...

2008-04-26T19:23:44Z

New page: ==Definition== The '''modulus map''', denoted <math>| \cdot |</math>, is a map <math>\mathbb{C} \to [0,\infty)</math>, denoted by: <math>z \mapsto |z|</math> It is defined as follows. I...

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==Definition==

The '''modulus map''', denoted <math>| \cdot |</math>, is a map <math>\mathbb{C} \to [0,\infty)</math>, denoted by:

<math>z \mapsto |z|</math>

It is defined as follows. If <math>z = x + iy</math> is a [[complex number]] with <math>x,y</math> being respectively the [[real part]] and [[imaginary part]], then:

<math>|z| = \sqrt{x^2 + y^2}</math>

==Facts==

The modulus map is an open map with respect to the usual topologies on <math>\mathbb{C}</math> and <math>[0,\infty)</math>. Note that it is ''not'' an open map if thought of as a map <math>\mathbb{C} \to \R</math>.

Modulus map - Revision history

Vipul: 1 revision

Vipul: New page: ==Definition== The '''modulus map''', denoted | \cdot |, is a map \mathbb{C} \to [0,\infty), denoted by: z \mapsto |z| It is defined as follows. I...

Vipul: New page: ==Definition== The '''modulus map''', denoted $| \cdot |$ , is a map $\mathbb{C} \to [0,\infty)$ , denoted by: $z \mapsto |z|$ It is defined as follows. I...