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# Urgent help with imaginary numbers? watch

1. 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

thanks
2. (Original post by liemluji)
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

thanks
is a variable. It's like me telling you to check whether is root of the quadratic equation . You have two options of doing this, you can either substitute into the LHS and see that it evaluates to , or you could solve the quadratic equation and check that one of the roots is .

Use this logic here as well. Either plug into your quadratic and see if it evaluates to or solve it using the quadratic equation and see if one of your roots is indeed .
3. (Original post by Zacken)
is a variable. It's like me telling you to check whether is root of the quadratic equation . You have two options of doing this, you can either substitute into the LHS and see that it evaluates to , or you could solve the quadratic equation and check that one of the roots is .

Use this logic here as well. Either plug into your quadratic and see if it evaluates to or solve it using the quadratic equation and see if one of your roots is indeed .
THank you so much! I managed to solve it
4. (Original post by liemluji)
THank you so much! I managed to solve it

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