SOLUTION: Find all solutions of the equation and express them in the form (a+bi) z + 4 + 12/z = 0 Thanks :)

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Question 263370: Find all solutions of the equation and express them in the form (a+bi)
z + 4 + 12/z = 0
Thanks :)
Found 2 solutions by drk, richwmiller:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is our original equation:
z+%2B+4+%2B+12%2Fz+=+0+
step 1 - multiply by z to get
z%5E2+%2B+4z+%2B+12+=+0
using the quadratic, we get
x+=+%28-4+%2B-+sqrt%2816-4%2A1%2A12%29%29%2F%282%29
which becomes
x+=+%28-4+%2B-+sqrt%28-32%29%29%2F%282%29
and then
x+=+%28-4+%2B-+4isqrt%282%29%29%2F%282%29
canceling, we get
x+=+-2+%2B-+2isqrt%282%29

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Put everything over z
%28z%5E2%2B4z%2B12%29%2Fz+=+0
z=-2.-2.82843i
z=-2.+2.82843i