Question

find x and y if (x+iy)(3+2i)=1+i

Answer 1

compare on both sides real and imaginary parts

Answer 2

Concept

To solve the product for (a+b)(c+d)=a(c+d)+b(c+d)

Given

The equation given is (x+iy)(3+2i)=1+i

Find

We need to find the values of x and y

Solution

The equation given is (x+iy)(3+2i)=1+i

Therefore

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

Now multiply x with 3 and 2i and iy with 3 and 2i

3x + 2ix +3iy +2i^2=1+i

We know that i^2=-1

So the equation formed is

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

Comparing the real imaginary parts

3x-2y=1

2x+3y=1

3x-2y-1=0

2x+3y-1=0

Therefore

x/2+3 = y/-2+3 = 1/9+4

x/5 = y = 1/13

Thefore

x=5/13 , y=1/13

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

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