Question

If x and y are reals and (3y + 2) + i(x + 3y) = 0 , find the values of x and y.
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Answer 1

Firstly we will break right hand side in complex number form as every real number can be break down in its Complex form then after comparing the imaginary and real parts of both sides we will get value of x and y on solving them very easily as following:-)

$(3y - 2) + \iota(x - 3y) = 0$

lt can be written as

$(3y + 2) + \iota(x - 3y) = 0 + 0 \iota$

Now ,by comparing real and imaginary parts of both sides we get ;

$3y - 2 = 0 \\ \implies \:y = \frac{2}{3} \: \: \: \: \: \: \: \: \: \: \boxed{\boxed{ANSWER}}$

also

$x - 3y = 0$

So by putting value of y

$x - 3 \times \frac{2} {3} = 0 \\ \implies \: x - 2 = 0 \\ \implies \: x = 2\: \: \: \: \: \: \: \: \: \: \boxed{\boxed{ANSWER}}$