SOLUTION: I need help with finding the complex number z that satisfies this equation: z*(2-i)=3+i Thank you :)

Question 543659: I need help with finding the complex number z that satisfies this equation: z*(2-i)=3+i Thank you :)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
z*(2-i) = 3 + i
Divide both sides by (2-i)
z =
multiply by the conjugate of the denominator over itself, (same as mult by 1)
z = *
FOIL
z =
we know i^2 = -1
z = =
which is
z =
cancel the 5
z = 1 + i
:
:
Confirm this; replace (1+i) for z in the original equation
(1+i)*(2-i) = 3 + i
FOIL
2-i+2i-i^2 = 3 + i
2 + i -(-1) = 3 + i
3 + i + 2 = 3 + i
3 + i = 3 + i; success!
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