Answer:
[tex]y^2+49=(y-7i)(y+7i)[/tex]
Step-by-step explanation:
Given : Expression [tex]y^2+49[/tex]
To find : Factor the expression over the complex numbers ?
Solution :
To factor the expression we equate it to zero and find the values of y,
[tex]y^2+49=0[/tex]
Subtract 49 both side,
[tex]y^2=-49[/tex]
Taking root both side,
[tex]y=\sqrt{-49}[/tex]
We know, [tex]\sqrt{-1}=i,\ \sqrt{49}=7[/tex]
[tex]y=\pm 7i[/tex]
The factors are [tex](y-7i)(y+7i)[/tex]
Therefore, [tex]y^2+49=(y-7i)(y+7i)[/tex]
