determine the values of x and y
 
 
(1+i)x - 2i/3+i  +  (2-3i)y +i/3-i  =  i
where i = iota
 

Asked by dalbirgolagarh | 8th Jul, 2016, 06:16: PM

Expert Answer:

begin mathsize 12px style fraction numerator left parenthesis 1 plus straight i right parenthesis straight x minus 2 straight i over denominator 3 plus straight i end fraction plus fraction numerator left parenthesis 2 minus 3 straight i right parenthesis straight y plus straight i over denominator 3 minus straight i end fraction equals straight i
rightwards double arrow fraction numerator left square bracket left parenthesis 1 plus straight i right parenthesis straight x minus 2 straight i right square bracket left parenthesis 3 minus straight i right parenthesis plus left square bracket left parenthesis 2 minus 3 straight i right parenthesis straight y plus straight i right square bracket left parenthesis 3 plus straight i right parenthesis over denominator 3 squared minus straight i squared end fraction equals straight i
rightwards double arrow fraction numerator left square bracket straight x plus ix minus 2 straight i right square bracket left parenthesis 3 minus straight i right parenthesis plus left square bracket 2 straight y minus 3 iy plus straight i right square bracket left parenthesis 3 plus straight i right parenthesis over denominator 9 plus 1 end fraction equals straight i
rightwards double arrow fraction numerator 3 straight x plus 3 ix minus 6 straight i minus ix minus straight i squared straight x plus 2 straight i squared plus 6 straight y minus 9 iy plus 3 straight i plus 2 iy minus 3 straight i squared straight y plus straight i squared over denominator 10 end fraction equals straight i
rightwards double arrow fraction numerator 3 straight x plus 3 ix minus 6 straight i minus ix plus straight x minus 2 plus 6 straight y minus 9 iy plus 3 straight i plus 2 iy plus 3 straight y minus 1 over denominator 10 end fraction equals straight i
rightwards double arrow 3 straight x plus 3 ix minus 6 straight i minus ix plus straight x minus 2 plus 6 straight y minus 9 iy plus 3 straight i plus 2 iy plus 3 straight y minus 1 equals 10 straight i
rightwards double arrow 3 straight x plus 3 ix minus 6 straight i minus ix plus straight x minus 2 plus 6 straight y minus 9 iy plus 3 straight i plus 2 iy plus 3 straight y minus 1 minus 10 straight i equals 0
rightwards double arrow left parenthesis 3 straight x plus straight x minus 2 plus 6 straight y plus 3 straight y minus 1 right parenthesis plus left parenthesis 3 ix minus 6 straight i minus ix minus 9 iy plus 3 straight i plus 2 iy minus 10 straight i right parenthesis equals 0
rightwards double arrow left parenthesis 4 straight x plus 9 straight y minus 3 right parenthesis plus straight i left parenthesis 3 straight x minus 6 minus straight x minus 9 straight y plus 3 plus 2 straight y minus 10 right parenthesis equals 0
rightwards double arrow left parenthesis 4 straight x plus 9 straight y minus 3 right parenthesis plus straight i left parenthesis 2 straight x minus 7 straight y minus 13 right parenthesis equals 0
Equating space real space and space imaginary space parts
rightwards double arrow 4 straight x plus 9 straight y minus 3 equals 0 rightwards double arrow 4 straight x plus 9 straight y equals 3... left parenthesis straight i right parenthesis
and space 2 straight x minus 7 straight y minus 13 equals 0 rightwards double arrow 2 straight x minus 7 straight y equals 13.... left parenthesis ii right parenthesis
Multiply space the space second space equation space by space 2 space and space subtract space it space from space the space first space equation.
4 straight x plus 9 straight y minus 4 straight x plus 14 straight y equals 3 minus 26
23 straight y equals negative 23 rightwards double arrow straight y equals negative 1
Substitute space straight y equals negative 1 space in space left parenthesis straight i right parenthesis comma space 4 straight x plus 9 straight y equals 3.
4 straight x plus 9 left parenthesis negative 1 right parenthesis equals 3 rightwards double arrow 4 straight x minus 9 equals 3 rightwards double arrow 4 straight x equals 12 rightwards double arrow straight x equals 3
Hence comma space straight x space equals space 3 space and space straight y space equals space minus 1.


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Answered by Rebecca Fernandes | 10th Jul, 2016, 11:07: PM