Question

Which answer is the product of _____ and its conjugate

Answer 1

ANSWER


`(11)/(9)`

Step-by-step explanation

The conjugate of


`- ( √(2) )/(3) + i`


is



`- ( √(2) )/(3) - i`

The product is



`( - ( √(2) )/(3) + i)( - ( √(2) )/(3) - i)`



We apply difference of two squares to obtain,



`= {( - ( √(2) )/(3) )}^(2) - {i}^(2) )`


Recall that,


`{i}^(2) = - 1`

This implies that,


`= ( (2)/(9) - ( - 1))`



`= (2)/(9) + 1`



`= (11)/(9)`