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2 years ago

May I know the values of x and y of the following equation?(5-3i)(x-yi) = 3(x+2yi)+1-2i

Mathematics

1 answer:

gogolik [260]2 years ago

3 0

Answer:

(x, y) = (17/31, 1/31)

Step-by-step explanation:

Simplify the given equation, then equate real parts and equate imaginary parts. This will give you two equations in the two unknowns.

<h3>simplify</h3>

(5 -3i)(x -yi) = 3(x +2yi) +1 -2i

5x -5yi -3xi +3yi² = 3x +6yi +1 -2i

(5x -3y) +i(-5y -3x) = (3x +1) +i(6y -2)

<h3>equate real, imaginary parts</h3>

This resolves to the two equations ...

5x -3y = 3x +1
-5y -3x = 6y -2

<h3>solve the system</h3>

Putting these equations into general form gives ...

2x -3y -1 = 0

3x +11y -2 = 0

Using the "cross multiplication method" to solve these equations, we get ...

x = ((-3)(-2) -(11)(-1))/(2(11) -3(-3)) = 17/31

y = ((-1)(3) -(-2)(2))/31 = 1/31

The values of x and y that satisfy this equation are ...

(x, y) = (17/31, 1/31)

_____

You can read more about the cross multiplication method here.

brainly.com/question/26397343

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May I know the values of x and y of the following equation?(5-3i)(x-yi) = 3(x+2yi)+1-2i​

May I know the values of x and y of the following equation?(5-3i)(x-yi) = 3(x+2yi)+1-2i