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Hi

Solve the equation for x and y: (x - iy) (2 + 3i) = x+2i / 1-i

 LHS

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

RHS

(x+2i)(1+i)/(1-i) ( 1+i)

=(x-2) / 2+ i(x+2)/2--------- (ii)

From (i) and (ii),

2x+3y=(x-2)/2                       and 3x-2y =(x+2)/2

⇒3x+6y = -2  -----(iii)     and 5x-4y=2--------(iv)

On solving (iii) and (iv), we get,

x= 2/21    and      y = -8/21

 

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This is correct.using the value of x calculate y

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On LHS (x-iy)(2+3i) Multiply 2x-2iy+3ix-3yi^^2. (We know i^^2 = -1) 2x -2iy +3ix +3y 2x+3y +i(3x-2y) --------(1) On RHS x+2i ÷ 1-i Now rationalize 1-i (x+2i)(1+i) ÷ (1-i)(1+i) x+2i+xi+2i^^2 ÷ (1)^^2-(i)^^2. (We know i^^2 = -1) Therefore: x+2i+xi-2 ÷ 1-(-1) x-2+i(x+2) ÷ 2 x-2 ÷ 2 + i(x+2) ÷ 2 ---------(2) From (1) & (2) 2x+3y = x-2 ÷ 2. &. 3x-2y =x+2 ÷ 2 4x+6y = x-2. &. 6x-4y = x+2 3x +6y = -2. ----(3) &. 5x-4y = 2------(4) Equate both (3) &(4) by each other Divide by 2 in eqn (3) & divide 3 in eqn (4) 6x+12y =-4 15x-12y =6 ------------------ 21x = 2 Therefore : x= 2÷21 Put value of x in eqn (4) Therefore : value of y=-8÷21
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