document.write( "Question 540921: If i represents the imaginary unit, what is the ordered pair of real numbers (x, y) for which x + xi + y – yi = -1 + 7i ?
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Algebra.Com's Answer #353911 by Theo(13342)\"\" \"About 
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x = 3
\n" ); document.write( "y = -4
\n" ); document.write( "here's why:
\n" ); document.write( "your equation is:
\n" ); document.write( "x + xi + y - yi = -1 + 7i
\n" ); document.write( "when you're dealing with complex numbers, the real parts are added together and the imaginary parts are added together.
\n" ); document.write( "this means tht:
\n" ); document.write( "x + y = -1
\n" ); document.write( "xi - yi = 7i
\n" ); document.write( "you can factor out the i in the second equation to get:
\n" ); document.write( "(x - y)i = 7i
\n" ); document.write( "if you divide both sides of this equation by i, you get:
\n" ); document.write( "x - y = 7
\n" ); document.write( "you now have 2 equations in x and y that need to be solved simultaneously.
\n" ); document.write( "they are:
\n" ); document.write( "x + y = -1
\n" ); document.write( "x - y = 7
\n" ); document.write( "if you add these 2 equations together you get:
\n" ); document.write( "2x = 6 (the + y and the - y cancel out).
\n" ); document.write( "if you divide both sides by 2 you get:
\n" ); document.write( "x = 3.
\n" ); document.write( "you can susbtitute in either of the 2 equations to get:
\n" ); document.write( "y = -4
\n" ); document.write( "subgstituting in the 2 equations, you get:
\n" ); document.write( "x + y becomes 3 + (-4) which is equal to 1, confirming the first equation in x and y is true.
\n" ); document.write( "x - y becomes 3 - (-4) which is equal to 7, confirming the second equation in x and y is true.
\n" ); document.write( "this confirms the values for x and y are good.
\n" ); document.write( "you can now subgstitute in your original equations to confirm that you will get the answer you desire.
\n" ); document.write( "the original equation is:
\n" ); document.write( "x + xi + y – yi = -1 + 7i
\n" ); document.write( "substitute 3 for x and -4 for y to get:
\n" ); document.write( "3 + 3i + (-4) - (-4i) = -1 + 7i
\n" ); document.write( "simplify the left side of the equation to get:
\n" ); document.write( "3 + 3i - 4 + 4i = -1 + 7i
\n" ); document.write( "simplify further to get:
\n" ); document.write( "-1 + 7i = -1 + 7i
\n" ); document.write( "this confirms the values for x and y are good.
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