Q. 21 A4.7( 8 Votes )

Find the real values of x and y for which:

(1 – i) x + (1 + i) y = 1 – 3i

Answer :

(1 – i) x + (1 + i) y = 1 – 3i

x – ix + y + iy = 1 – 3i


(x + y) – i(x – y) = 1 – 3i


Comparing the real parts, we get


x + y = 1 …(i)


Comparing the imaginary parts, we get


x – y = -3 …(ii)


Solving eq. (i) and (ii) to find the value of x and y


Adding eq. (i) and (ii), we get


x + y + x – y = 1 + (-3)


2x = 1 – 3


2x = -2


x = -1


Putting the value of x = -1 in eq. (i), we get


(-1) + y = 1


y = 1 + 1


y = 2


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