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## Homework Statement

So I have been having trouble with finding the proper eigen vector for a complex eigen value

for the matrix A=(-3 -5)

. .........................(3 1)

had a little trouble with formating this matrix sorry

The eigen values are -1+i√11 and -1-i√11

## The Attempt at a Solution

using A

**Y**-λ

**Y**=0 (where

**Y**is a vector (x, y) I obtain two different equations :

3x+y-(-1+i√11)y=0 and -3x-5y-(-1+i√11)x=0

these simplify too: 3x=(i√11 -2)y and 5y=(-2-i√11)x

no I know that the right eigen vecotor is (i√11 -2,3) but why isnt (5, -2-i√11) one? they both work when I plug them in.