SOLUTION: Evaluate the expression and write the result in the form a + bi. 1/(2-4i)-1/(6-2i) =____+ ____i I can't figure this out. Any help appreciated!

Algebra ->  Equations -> SOLUTION: Evaluate the expression and write the result in the form a + bi. 1/(2-4i)-1/(6-2i) =____+ ____i I can't figure this out. Any help appreciated!      Log On


   

Question 124331: Evaluate the expression and write the result in the form a + bi.
1/(2-4i)-1/(6-2i)
=____+ ____i
I can't figure this out. Any help appreciated!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate the expression and write the result in the form a + bi.
1/(2-4i)-1/(6-2i)
[6-2i-(2-4i)]/[(2-4i)(6-2i)]
= (4+2i)/(12-8-28i)
= (4+2i)/(4-28i)
Reduce:
= (2+i)/(2-14i)
Multiply numerator and denominator by (2+14i) to get:
=[(2+i)(2+14i)]/[200]
= [(4-14+30i)]/200
= [-10+30i]/200
= (-10/200) + (30/200)i
= -0.05 + 0.15i
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Cheers,
Stan H.
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