Lesson Vocabulary

• imaginary unit
• imaginary number
• complex number
• pure imaginary number
• complex number plane
• absolute value of a complex number
• complex conjugates

Take Note Key Concept: Square Root of a Negative Real Number

Algebra

For any positive number a,

− a = − 1 ⋅ a = − 1 ⋅ a = i a . square root of negative eh end root , equals . square root of negative 1 dot eh end root . equals , square root of negative 1 end root , dot square root of eh equals i square root of eh .

Example

− 5 = i 5 square root of negative 5 end root , equals i square root of 5

Note that ( − 5 ) 2 = ( i 5 ) 2 = i 2 ( 5 ) 2 = − 1 ⋅ 5 = − 5 ( not  5 ) . open , square root of negative 5 end root , close squared . equals . open , i square root of 5 , close squared . equals , i squared . open square root of 5 close squared . equals negative 1 dot 5 equals negative 5 . open , not , 5 , close . .