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Find the values of $x$x​ and $y$y​ that satisfy the equation.$54-\frac{1}{7}yi=9x-4i$54−17​yi=9x−4i​$x=$x=​  6−iy63​+4i9​ and  $y=$y=​  63xi+28−378i

Question

Find the values of xxx​ and yyy​ that satisfy the equation.5417yi=9x4i54-\frac{1}{7}yi=9x-4i54−17​yi=9x−4i​x=x=x=​  6−iy63​+4i9​ and  y=y=y=​  63xi+28−378i

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Solution

The given equation is 5417yi=9x4i54-\frac{1}{7}yi=9x-4i.

First, we can separate the real and imaginary parts of the equation:

Real part: 54=9x54 = 9x, Imaginary part: 17y=4-\frac{1}{7}y = -4.

Solving these equations gives:

For the real part: x=549=6x = \frac{54}{9} = 6.

For the imaginary part: y=174=47y = \frac{1}{7} * 4 = \frac{4}{7}.

So, the solution to the equation is x=6x = 6 and y=47y = \frac{4}{7}.

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