Find the real values of x and y for which:x + 4yi = ix + y + 3

1.	Find the real values of x and y for which:x + 4yi = ix + y + 3
Answer» Given: x + 4yi = ix + y + 3 or x + 4yi = ix + (y + 3) Comparing the real parts, we get x = y + 3 Or x – y = 3 …(i) Comparing the imaginary parts, we get 4y = x …(ii) Putting the value of x = 4y in eq. (i), we get 4y – y = 3 ⇒ 3y = 3 ⇒ y = 1 Putting the value of y = 1 in eq. (ii), we get x = 4(1) = 4 Hence, the value of x = 4 and y = 1

Answer»

Given: x + 4yi = ix + y + 3

or x + 4yi = ix + (y + 3)

Comparing the real parts, we get

x = y + 3 Or x – y = 3 …(i)

Comparing the imaginary parts, we get

4y = x …(ii)

Putting the value of x = 4y in eq. (i), we get

4y – y = 3

⇒ 3y = 3

⇒ y = 1

Putting the value of y = 1 in eq. (ii), we get

x = 4(1) = 4

Hence, the value of x = 4 and y = 1

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