Question

Complex roots question

Answer 1

I'm solving Euler Cauchy equations where I needed to use the quadratic formula as it was too complicate to factor in my head so I got this. I know it's an imaginary number, but I need to simplify that down. Any ideas?

Answer 2

Yeah, how did you get root 3?

Answer 3

plz explain how you got that answer

Answer 4

I understand where i is from, not the 3 though!!

Answer 5

Also the real part of that root should be -0.5

Answer 6

Factor 192 into primes, then simplify the imaginary term. Cancel the numerator and denominator, and you've got it.\[192=2(96)=2^2(48)=2^6(3) \implies \sqrt{192}=8\sqrt3\] \[\implies \frac{-4 \pm \sqrt{-192}}{8}=-\frac{1}{2} \pm i \sqrt3\]