(→Definition) |
(→Properties) |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 3: | Line 3: | ||
== Definition== | == Definition== | ||
| + | <pre> | ||
Complex number is the combination of real number and imaginary number. It's basic form is a+bi, Where | Complex number is the combination of real number and imaginary number. It's basic form is a+bi, Where | ||
a is the real part and bi is the imaginary part. | a is the real part and bi is the imaginary part. | ||
| + | |||
i is the unit for imaginary number. In a complex coordinate, a+bi is point(a,b). The distance between | i is the unit for imaginary number. In a complex coordinate, a+bi is point(a,b). The distance between | ||
| − | this point and the origin is | + | this point and the origin is the square root of (a^2 + b^2). |
| + | |||
In the form a+bi, when b=0, the complex number belongs to real number; when a=0, the complex number | In the form a+bi, when b=0, the complex number belongs to real number; when a=0, the complex number | ||
belongs to imaginary number; when they both are not zero, it belongs to complex region. | belongs to imaginary number; when they both are not zero, it belongs to complex region. | ||
| + | |||
The triangular form of a complex number is Z=r(cosx + isinx). r is the distance between point Z and | The triangular form of a complex number is Z=r(cosx + isinx). r is the distance between point Z and | ||
the origin on a complex coordiante. rcosx is real part and irsinx is the imaginary part. | the origin on a complex coordiante. rcosx is real part and irsinx is the imaginary part. | ||
| + | </pre> | ||
| + | |||
| + | |||
| + | == Properties == | ||
| + | :* Addition: <math>\,(a + bi) + (c + di) = (a + c) + (b + d)i</math> | ||
| + | :* Subtraction: <math>\,(a + bi) - (c + di) = (a - c) + (b - d)i</math> | ||
| + | :* Multiplication: <math>\,(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad)i</math> | ||
| + | :* Division: <math>\,\frac{(a + bi)}{(c + di)} = \left({ac + bd \over c^2 + d^2}\right) + \left( {bc - ad \over c^2 + d^2} \right)i\,,</math> | ||
| + | where ''c'' and ''d'' are not both zero. | ||
| + | |||
| + | **Source for wikipedia: [[http://en.wikipedia.org/w/index.php?title=Complex_number&action=edit§ion=4]] | ||
Latest revision as of 16:26, 2 September 2008
Review of Complex Number
Definition
Complex number is the combination of real number and imaginary number. It's basic form is a+bi, Where
a is the real part and bi is the imaginary part.
i is the unit for imaginary number. In a complex coordinate, a+bi is point(a,b). The distance between
this point and the origin is the square root of (a^2 + b^2).
In the form a+bi, when b=0, the complex number belongs to real number; when a=0, the complex number
belongs to imaginary number; when they both are not zero, it belongs to complex region.
The triangular form of a complex number is Z=r(cosx + isinx). r is the distance between point Z and
the origin on a complex coordiante. rcosx is real part and irsinx is the imaginary part.
Properties
- Addition: $ \,(a + bi) + (c + di) = (a + c) + (b + d)i $
- Subtraction: $ \,(a + bi) - (c + di) = (a - c) + (b - d)i $
- Multiplication: $ \,(a + bi) (c + di) = ac + bci + adi + bd i^2 = (ac - bd) + (bc + ad)i $
- Division: $ \,\frac{(a + bi)}{(c + di)} = \left({ac + bd \over c^2 + d^2}\right) + \left( {bc - ad \over c^2 + d^2} \right)i\,, $
where c and d are not both zero.
- Source for wikipedia: [[1]]
