confirmation on complex numbers

[vixity]

the question is; solve

z^2 + (2+4i)z -11 -2i = 0

well i did it and my answer is z= 6 + 2i and z= -6 -2i which i know is WRONG right?

BUT say if it is CORRECT, is that my final answer? or do i have to sub that in with something because i am sure you have to.

So can someone give me the correct answer and the steps involve as well as i want to crack this thing once and for all.

[krtxmrtz]

the question is; solve

z^2 + (2+4i)z -11 -2i = 0

well i did it and my answer is z= 6 + 2i and z= -6 -2i which i know is WRONG right?

BUT say if it is CORRECT, is that my final answer? or do i have to sub that in with something because i am sure you have to.

So can someone give me the correct answer and the steps involve as well as i want to crack this thing once and for all.

The correct answer is

z = 2 - i

and

z = -4 -3i

EDIT:
Hang on there while I try to find a useful link...

[krtxmrtz]

This may be useful:

http://www.vibrationdata.com/arbit_root.htm

[vixity]

The correct answer is

z = 2 - i

and

z = -4 -3i

EDIT:
Hang on there while I try to find a useful link...

yeah and what do you do now with the two answers for z. Do you sub it in the question?cause if you do you solve for i correct?

[Glaysher]

The answers for z are the answers to the whole question. i is a constant, you can't solve for it.

[zaza]

And just to be sure it is clear, i is used to indicate imaginary numbers. It is defined as sqrt(-1). So you can't "solve" for it, it would be like solving for 6.


zaza

[krtxmrtz]

And, as a math teacher I had used to say, if you don't know how to calculate sqr(-1) then what you do is
"you call the problem the solution", so sqr(-1) = i and that's all there is to that.