Find the values of $x$x and $y$y that satisfy the equation.$54-\frac{1}{7}yi=9x-4i$54−17yi=9x−4i$x=$x= 6−iy63+4i9 and $y=$y= 63xi+28−378i
Question
Find the values of and that satisfy the equation.
54 - \frac{1}{7} y i = 9x - 4i
where
x = 6 - \frac{iy}{63} + \frac{4i}{9}
and
y = 63xi + 28 - 378i
Solution
The given equation is .
First, we can separate the real and imaginary parts of the equation:
Real part: , Imaginary part: .
Solving these equations gives:
For the real part: .
For the imaginary part: .
So, the solution to the equation is and .
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