# Thread: Complex Numbers help

1. ## Re: Complex Numbers help

Originally Posted by kmalik001
Thank you so much!
I understand it.

I am also kind of stumped on this question.

Determine the only real values a, b, c and d such that the equation:
z^4 + az^3 + bz^2 + cz + d = 0
has both z1 and z2 as roots.

I don't really get what this is asking.
Good!

I guess this requires a bit of additional knowledge about polynomial equations with real coefficients and complex roots.

A polynomial that has both z1 and z2 as its roots, must be of the form:

(z-z1)(z-z2)(...) = 0

If such an equation has only real coefficients, that implies that not only z1 must be a root, but also its conjugate z1*.
(I suspect that is somewhere in your notes.)

In other words, your equation must be of the form:

$\displaystyle (z-z_1)(z-z_1^*)(z-z_2)(z-z_2^*) = 0$

If you expand this, which coefficients do you get?

2. ## Re: Complex Numbers help

Originally Posted by Plato
@ ILikeSerena
I don't care that you responded to this thread.
Ah well, that's okay, as long as you don't mind if I slice your comments to pieces (assuming you give me the opportunity as you did this time round).

3. ## Re: Complex Numbers help

Ah yes I see what you are doing. So when I expanded it I get z^4 + 4z^3 + 0z^2 -200z + 500. Which I hope is right.
I expanded (z^2 -6z + 10)(z^2 +10 z +50), which I know are right since their solutions are the z1, z2 and their conjugates.

Thanks to both of you once again

4. ## Re: Complex Numbers help

Originally Posted by kmalik001
Ah yes I see what you are doing. So when I expanded it I get z^4 + 4z^3 + 0z^2 -200z + 500. Which I hope is right.
I expanded (z^2 -6z + 10)(z^2 +10 z +50), which I know are right since their solutions are the z1, z2 and their conjugates.

Thanks to both of you once again
Yep. That is right!

5. ## Re: Complex Numbers help

So there is another complex number question.

u = −1 + j√3 and v = √3 − j

Let a be a real scaling factor. Determine the value(s) of a such that
|u −a/v | = 2√2

So this is what I am doing I am kind of stuck and wondering if I am on the right track.

6. ## Re: Complex Numbers help

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