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July 24th, 2017, 02:39 PM   #1
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Need help - Problem related to complex numbers...

So, I need help with this problem guys. Here it goes...

The real and imaginary parts of the complex number $\displaystyle z=x+iy$ satisfy the equation $\displaystyle \left( 2-i \right) x-\left( 1+3i \right) y-7=0$.

Find the value of x and the value of y.

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** Thanks in advance. Please leave your workings, I'd appreciate it.
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July 24th, 2017, 02:52 PM   #2
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The equation is equivalent to $2x - y - 7 - (x + 3y)i = 0$, so $2x - y - 7 = x + 3y = 0$.
It follows that $(x,\,y) = (3,\,-1)$.
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July 24th, 2017, 03:00 PM   #3
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I see, so the idea was to set up a simultaneous equation.

It was the first problem like it in the textbook. Cheers.
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