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July 24th, 2017, 02:39 PM  #1 
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 470 Thanks: 40  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 $\displaystyle \left( 2i \right) x\left( 1+3i \right) y7=0$. Find the value of x and the value of y.  ** Thanks in advance. Please leave your workings, I'd appreciate it. 
July 24th, 2017, 02:52 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,116 Thanks: 1910 
The equation is equivalent to $2x  y  7  (x + 3y)i = 0$, so $2x  y  7 = x + 3y = 0$. It follows that $(x,\,y) = (3,\,1)$. 
July 24th, 2017, 03:00 PM  #3 
Senior Member Joined: Jul 2013 From: United Kingdom Posts: 470 Thanks: 40 
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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