Question

find the values of x and y if (1+i) (x-3yi)=7+i​

Answer 1

Answer:

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.

Answer 2

Answer:

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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.