Difference between revisions of "Absolute value"
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[[Complex number]]s also have an absolute value. If <math>z = x+iy</math> is a complex number with real part <math>x</math> and imaginary part <math>y</math>, then <math>|z| = \sqrt{x^2 + y^2}</math>. If we represent <math>z</math> as a point in the complex plane with coordinates <math>(x,y)</math>, then <math>|z|</math> is the distance from this point to the origin. The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality. | [[Complex number]]s also have an absolute value. If <math>z = x+iy</math> is a complex number with real part <math>x</math> and imaginary part <math>y</math>, then <math>|z| = \sqrt{x^2 + y^2}</math>. If we represent <math>z</math> as a point in the complex plane with coordinates <math>(x,y)</math>, then <math>|z|</math> is the distance from this point to the origin. The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality. | ||
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[[Category:Algebra]] | [[Category:Algebra]] | ||
+ | [[Category:Mathematics]] |
Revision as of 04:43, March 16, 2011
The absolute value of a number is a measure of the size of that number. The absolute value of is written .
- If is a positive number, then .
- If is a negative number, then .
- If then .
Absolute value has several useful properties. One is the multiplicative property. If and are two numbers, then . Another is the triangle inequality, which is the fact that . For example, if and , then , while . In this case, the triangle inequality is the fact that 2 is not more than 8.
Complex numbers also have an absolute value. If is a complex number with real part and imaginary part , then . If we represent as a point in the complex plane with coordinates , then is the distance from this point to the origin. The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.