Question

Find x and y if (x+y)-i(3x+2y)=5+2i

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.

Answer 2

SOLUTION

GIVEN

$\sf{(x + y) - i(3x + 2y)} = 5 + 2i$

TO DETERMINE

The value of x and y

EVALUATION

Here it is given that

$\sf{(x + y) - i(3x + 2y)} = 5 + 2i$

Comparing real parts and Imaginary parts in both sides we get

x + y = 5 - - - - - - - (1)

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

Equation 2 - 2 × Equation 1 gives

x = - 2 - 10

⇒ x = - 12

From Equation 1 we get

y = 5 - x = 5 + 12 = 17

FINAL ANSWER

x = - 12 , y = 17

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