Solving a matrix with complex numbers help

[subopolois]

Homework Statement

ive been given this system of equations and told to solve it:
x+2y+2z=-3
2x+y+z=0
x-y-iz=i

Homework Equations

all elementary row operations

The Attempt at a Solution

1 2 2|-3
2 1 1| 0 row2-row1 then row2 x -1/3
1-1-i| i

1 2 2|-3
0 1 1|-2 row3-row1 then row3+3 x row2
1-1-i|i

1 2 2|-3
0 1 1|-2
0 0 5-i|-3+i

at this point I am stuck, i know i have to get it in reduced row echelon form, but that 5-i has got me scratching my head, and somehow i know i have to get it to be 1 in order to reduce the other rows.

 

[HallsofIvy]

You do exactly what you do with real numbers! Divide both sides by 5-i. If you want to get (-3+i)/(5- i) in "a+ bi" form, try multiplying both numerator and denominator by 5+ i.