Urgent help with imaginary numbers?

Hi I'm taking further pure and i have a question about imaginary numbers.
It would be thankful if you'd helped me

Verify that 3+i is a root of the quadratic equation

z^2-(2+4i)z+8i-6=0

I'm not quite sure if z in the question is just a letter or z=x+iy

please help me

thanks

$z$ is a variable. It's like me telling you to check whether $x=3$ is root of the quadratic equation $x^2 -8x + 15 = 0$. You have two options of doing this, you can either substitute $x=3$ into the LHS and see that it evaluates to $0$, or you could solve the quadratic equation and check that one of the roots is $x=3$.

Use this logic here as well. Either plug $z =3+i$ into your quadratic and see if it evaluates to $0$ or solve it using the quadratic equation and see if one of your roots is indeed $3+i$.

THank you so much! I managed to solve it