SOLUTION: 1/z= (1/(3-6i)) + (1/(5+4i)) please show work thanks!!!

Question 776165: 1/z= (1/(3-6i)) + (1/(5+4i)) please show work thanks!!!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1/z= (1/(3-6i)) + (1/(5+4i))
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1/z = (3+6i)/(9+36) + (5-4i)/(25+16)
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1/z = (1+2i)/15 + (5-4i)/41
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1/z = [41(1+2i) + 15(5-4i)]/(15*41)
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1/z = (116+22i)/(15*41)
---
z/1 = 56/(116+22i)
----
z = 56(116-22i)/(116^2+22^2)
----
z = [56(116-22i)/13940]
etc.
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Cheers,
Stan H.
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