Find the value of the expression : {x}^(2) + 2xy + {y}^(2) y = (3 + i )/(i) \\ x = 2 + 3i ​

Question

Find the value of the expression :


`{x}^(2) + 2xy + {y}^(2)`



`y = (3 + i )/(i) \\ x = 2 + 3i`
​

Answer 1

Answer: x² + 2xy + y² = 9

x² + 2xy + y² = (x + y)²

with x = 2 + 3i and y =
`(3+i)/(i)`, we have:

`(x + y)^(2)=(2+3i+(3+i)/(i))^(2)\\\\=((2i+3i^(2)+3+i )/(i))^(2)\\\\=((3i-3+3)/(i))^(2) \\\\=((3i)/(i))^(2)\\\\=3^(2)=9`

Explanation: