# Chapter 3 : Absolute Value

### Topics covered in this snack-sized chapter:

#### Absolute Value arrow_upward

• The absolute value of a real number is its numerical value without regard to its sign.
• It is denoted as |number|.
• It is always non – negative.
• is the absolute value of both and • • • • The absolute value is related to the distance from the origin.
• The absolute value of a real or complex number is the distance from that number to the origin, along the real number line.

• #### Formal Definition arrow_upward #### Graph of the Modulus Function arrow_upward #### Properties of the Absolute Value Function arrow_upward The square root notation without sign represents the positive square root Non-negativity Positive-definiteness Multiplicativeness Subadditivity Symmetry Identity of indiscernibles (equivalent to positive-definiteness) Triangle inequality (equivalent to subadditivity) Preservation of division (equivalent to multiplicativeness) (equivalent to subadditivity)

#### Absolute Value of Complex Numbers arrow_upward

• The absolute value of a complex number is the distance from to the origin
• • For any complex number
•  • Where and are real numbers, the absolute value or modulus of is
• denoted and is defined as
• • The absolute value of a real number is equal to its absolute value when considered as a complex number
• #### Operations on the Absolute Value arrow_upward

 Case 1 and are both positive: 0 so | xy |= 0 = ( 0 )( 0 )= | x || y | #### Thank You from Kimavi arrow_upward

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