Q. 21 E5.0( 4 Votes )

Find the real values of x and y for which:

= (1 – i)

Answer :

Given:


x + 3i = (1 – i)(2 + iy)


x + 3i = 1(2 + iy) – i(2 + iy)


x + 3i = 2 + iy – 2i – i2y


x + 3i = 2 + i(y – 2) – (-1)y [i2 = -1]


x + 3i = 2 + i(y – 2) + y


x + 3i = (2 + y) + i(y – 2)


Comparing the real parts, we get


x = 2 + y


x – y = 2 …(i)


Comparing the imaginary parts, we get


3 = y – 2


y = 3 + 2


y = 5


Putting the value of y = 5 in eq. (i), we get


x – 5 = 2


x = 2 + 5


x = 7


Hence, the value of x = 7 and y = 5


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