Complex number: Difference between revisions

Revision as of 11:52, 22 June 2006

The set of complex numbers is denoted by $\mathbb{C}$ . The complement of this set is $\mathbb{R}$ , the real numbers. All complex numbers can be divided into two parts, the real part, denoted by $\Re$ or simply $\mathrm{Re}$ , and the imaginary part, denoted by $\Im$ or simply $\mathrm{Im}$ .

The letters $z$ and $\omega$ are usually used to denote complex numbers.

Operations

Addition
Subtraction
Multiplication
Division
Absolute value/Modulus/Magnitude (denoted by $|z|$ ). This is the distance from the origin to the complex number when graphed.

Simple Example

If $z=a+bi$ and $\omega=c+di$ ,

$\mathrm{Re}(z)=a$ , $\mathrm{Im}(z)=b$
$|z|=\sqrt{a^2+b^2}$
$\mathrm{Re}(\omega)=c$ , $\mathrm{Im}(\omega)=d$
$|\omega|=\sqrt{c^2+d^2}$
$z+\omega=(a+c)+(b+d)i$
$z-\omega=(a-c)+(b-d)i$

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Complex number: Difference between revisions

Revision as of 11:52, 22 June 2006

Contents

Operations

Simple Example

Topics

See also

Revision as of 11:40, 22 June 2006 view source IntrepidMath (talk \| contribs) Administrators 197 edits mNo edit summary ← Older edit	Revision as of 11:52, 22 June 2006 view source Chess64 (talk \| contribs) 431 edits m Complex numbers moved to Complex number: singular Newer edit →
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