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:
If you expand this, which coefficients do you get?
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
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.