Question

(x+iy)(2-3i)=4+i find x and y​

Answer 1

Answer:

(x+iy)(2−3i)=4+i

2x−(3x)i+(2y)i−3yi

2

=4+i

Real

2x+3y

+

Imaginary

(2y−3x)

i=4+i

Comparing the real & imaginary parts,

2x+3y=4--------------------------(1)

2y−3x=1----------------------------(2)

Solving eq(1) & eq(2),

4x+6y=8

−9x+6y=3

13x=5⇒x=

13

5

y=

13

14

∴(x,y)=(

13

5

,

13

14

)

Answer 2

Step-by-step explanation:

Correct option is

C

(135,1314)

(x+iy)(2−3i)=4+i

2x−(3x)i+(2y)i−3yi2=4+i

Real2x+3y+Imaginary(2y−3x)i=4+i

Comparing the real & imaginary parts,

2x+3y=4--------------------------(1)

2y−3x=1----------------------------(2)

Solving eq(1)  &  eq(2),

4x+6y=8

−9x+6y=3

13x=5⇒x=135

y=1314

∴(x,y)=(135,1314)