Question

Find the value of X and y
1.x+i5y=ix+y+7
2.(2x+4i)(1+I)/(3-2i)=2+iy

Answer 1

Answer:

Here conjugate of 5+4i is 5-4i

and (a+2y)+i(2x-3y) is the conjugate of 5+4i

ie (x+2y)+i(2x-3y)=5-4i

comparing real parts and imaginary parts we get

x+2y=5 and 2x-3y=-4 _________ (1)

⇒x=5−2y

substituting value of x is (ii), we get

2(5-2y)-3y=-4

10-4y-3y=-4

⇒7y=14

⇒y=2.

from (1), x=5-2(2)=5-4

∴x=1

since x=1, y=2.