Relations and Functions

Relations and Functions

Question

Find the values of x and y, if.

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Answer
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#6 {main}</pre> = i
rightwards double arrow space space space space space space space space space space space space space space fraction numerator 3 straight x space plus space 3 ix space minus 6 straight i space minus space ix space minus straight i squared straight x space plus space 2 straight i squared space plus space 6 straight y space minus space 9 iy space plus space 3 straight i space plus space 2 iy space minus space 3 straight i squared straight y space plus space straight i squared over denominator 3 squared space minus space straight i squared end fraction space equals space straight i

rightwards double arrow space space space space space space space space space space space space space space space space fraction numerator 3 straight x space plus space 2 ix space minus space 3 straight i space plus space straight x space minus 2 space plus space 6 straight y space minus 9 iy space plus space 3 straight i space plus space 2 iy space minus space 3 straight i squared straight y space plus space straight i squared over denominator 9 space plus space 1 end fraction space equals space straight i
rightwards double arrow           (4x + 9y -3) + i (2x - 7y - 3) = 10i
Equating real and imaginary parts, we get
Re (z) : 4x + 9y - 3 = 0               rightwards double arrow     4x + 9y = 3                               ....(i)
Im (z) : 2x - 7y - 3 = 10              rightwards double arrow     2x - 7y = 13                               ...(ii)
Multipling (ii) by 2, we get
          4x - 14y = 26
Subtracting (iii) from (i), we get
23y = -23  rightwards double arrow y = -1
Using in (i), we get
         4x + 9(-1) = 3               rightwards double arrow      4x = 12  rightwards double arrow x =3
Hence,  x - 3 and y = -1

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