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If (5+6 i)/(3+4 i)=x+i y, then find the ...

If `(5+6 i)/(3+4 i)=x+i y`, then find the value of `x-y`.

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We have. .x+i y=(5+6 i)/(3+4 i)=(5+6 i)/(3+4 i) xx ((3-4 i))/((3-4 i))=(15-20 i+18 i+24)/(9+16)=(39-2 i)/(25).
.=(39)/(25)+(-2)/(25) i:
therefore x=(39)/(25), y=(-2)/(25) x-y=(39)/(25)-(-2)/(25)=(41)/(25).
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