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.
ok you are doing fine...continue....get the modulus of the complex number you found and then square it...and solve the quadratic equation that you will find...
finally you will get two solutions
a =2sqr(3)-2sqr(7) and a= 2sqr(7)-2sqr(3).
|z| = √(Re(z)2 + Im(z)2)
in this case:
Re(z) = (1/4)(-4 - a√3)
Im(z) = (1/4)(4√3 - a)
squaring, we have:
Re(z)2 = (1/16)(16 + 8a√3 + 3a2)
Im(z)2 = (1/16)(48 - 8a√3 + a2)
adding these together, we get:
Re(z)2 + Im(z)2 = (1/16)(64 + 4a2)
rather than deal with messy square roots, let's square both sides:
|z|2 = 2
(1/16)(64 + 4a2) = 2
64 + 4a2 = 32
4a2 + 32 = 0 <---this has no real solutions.
Thank you I have sucessfully learned the modulus method now
just one thing I wanted to point out |z|^2 = 2√2 so then a comes out to be +- 4.
and the question said it wanted to be a real scaling factor so thats perfect. Thank you once again