Question

Find real value of x and y, if (x+iy)(2+3i)=4+i

Answer 1

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Class 11

>>Applied Mathematics

>>Number theory

>>Complex Numbers

>>If (x + iy)(2 - 3i) = 4 + i...

Question

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If (x+iy)(2−3i)=4+i then (x, y) =

Easy

Solution

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Correct option is

C

(

13

5

,

13

14

)

(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

)