Question

If (x – 2) + iy = 3 + 4i then x + y is

Answer 1

Answer:

Step-by-step explanation:

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

​

)

Answer 2

Answer:

(x - 2) + iy = 3 + 4i

x - 2 + iy = 3 + 4i

first we need to find x

x = 3 + 4i +2 -iy

x = 5 +4i - iy ------> ( i )

we got x

now we need to find y

let find y from ( i )

x = 5 + 4i -iy

iy = 5 + 4i -x

y = 5 + 4i -x / I

we got x & y

now X + y

5 + 4i -iy + (5 +4i -x /I )