Q. 21 E5.0( 4 Votes )

# Find the real values of x and y for which: = (1 – i)

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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Evaluate:

(i) (iii) .

RS Aggarwal - Mathematics