Relations and Functions

Relations and Functions

Question

If Z1 = (x - 3y) - i (2x + y), and Z2 = -1 - 5i are equal,   find values of x a nd y.

Answer

Here,               Z1 = (x - 3y) -i(2x + y), Z2 = -1 - 5i
Now,                Z1 = Z2 rightwards double arrow Re(Z1) = Re (Z2) rightwards double arrow x-3y rightwards double arrowx  = -1                     ...(i)
               
and                  Z1 =Z2 rightwards double arrow1m(Z1) = 1m(Z2) rightwards double arrow - 5 = 2x - y rightwards double arrow2x + y = 5       ...(ii)             
Solving (i) and (ii) simultancously, we have
 
                    x = 2, y = 1

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