Question

find x and y in (x+iy)(3+2i)= 1+i​

Answer 1

Given :-

( x + iy ) ( 3 + 2i ) = 1 + i

To find :-

Value of x and y

Solution :-

⇒ ( x + iy ) ( 3 + 2i ) = 1 + i

⇒ x ( 3 + 2i ) + iy ( 3 + 2 i ) = 1 + i

⇒ 3x + 2xi + 3yi + 2i²y = 1 + i

⇒ 3x + 2xi + 3yi + 2(-1) y = 1 + i

⇒ 3x + 2xi + 3yi - 2y = 1 + i

⇒ ( 3x - 2y ) + ( 2xi + 3yi ) = 1 + i

⇒ ( 3x - 2y )i + ( 2x + 3y ) i = 1 + i

Now, by comparing LHS and RHS, we get the following two equations :

• 3x - 2y = 1 ( Equation 1. )
• 2x + 3y = 1 ( Equation 2. )

Now, we have two linear equations in the variable x and y, this seems to be quite easy to solve.

By multiplying equation (1) with 2 and equation (2) with 3, we get new two equations :

• 6x - 4y = 2 ( Equation 3. )
• 6x + 9y = 3 ( Equation 4. )

By subtracting equation (3) from equation (4), we get :

⇒ ( 6x + 9y ) - ( 6x - 4y ) = 3 - 2

⇒ 6x + 9y - 6x + 4y = 1

⇒ 9y + 4y = 1

⇒ 13y = 1

⇒ y = 1 / 13

Now substitute this value of y in equation (1)

⇒ 3x - 2y = 1

⇒ 3x - 2/13 = 1

⇒ 3x = 1 + 2/13

⇒ 3x = (13 + 2) / 13

⇒ 3x = 15 / 13

⇒ x = 15 / (13 × 3)

⇒ x = 5 / 13

Hence value of x is 5/13 and value of y is 1/13.