Find the values of $x$x and $y$y that satisfy the equation.$15-3yi=\frac{1}{2}x+2i$15−3yi=12x+2i$x=$x= −6yi+30−4i and $y=$y=

Question

Find the values of $x$ x and $y$ y that satisfy the equation. $15-3yi=\frac{1}{2}x+2i$ 15−3yi=12x+2i $x=$ x= −6yi+30−4i and $y=$ y=

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Solution

The given equation is $15-3yi=\frac{1}{2}x+2i$

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

Real part: $15 = \frac{1}{2}x$

Imaginary part: $-3y = 2$

Solving these two equations gives:

For the real part, multiply both sides by 2 to solve for x:

$2*15 = x$

$x = 30$

For the imaginary part, divide both sides by -3 to solve for y:

$2 / -3 = y$

$y = -2/3$

So, the solutions are $x = 30$ and $y = -2/3$ .

This problem has been solved

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