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Question

The real values of x and y for which the equation is (x+iy)(2-3i)=4+i is satisfied, are


A

x=513,y=813

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B

x=813,y=513

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C

x=513,y=1413

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D

None of these

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Solution

The correct option is C

x=513,y=1413


Compute the required values:

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

2x+i2y-i3x+3y=4+i2x+3y+i(2y-3x)=4+i

Comparing real and imaginary parts,

2x+3y=4……………..1

-3x+2y=1……………..2

Add 3×1 and 2×2,

6x+9y-6x+4y=12+2

13y=14

y=1413

Substitute the value of y in equation1,

2x+31413=4

2x=52-4213

x=513

Hence real value of x and y is 513 and 1413.

Hence, option (c) is the correct option.


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