SOLUTION: (2x+y) + (3-5x)i = 1 -7i solve for x & y I lumped the i's and the numbers together then squared everything to get {{{29x^2+4xy-104x+y^2-2y=-101 The answer is x=2 & y=-3,

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: (2x+y) + (3-5x)i = 1 -7i solve for x & y I lumped the i's and the numbers together then squared everything to get {{{29x^2+4xy-104x+y^2-2y=-101 The answer is x=2 & y=-3,       Log On


   

Question 154388This question is from textbook Advanced Mathematics
: (2x+y) + (3-5x)i = 1 -7i solve for x & y
I lumped the i's and the numbers together then squared everything to get
29x^2+4xy-104x+y^2-2y=-101
The answer is x=2 & y=-3, but I can't get there. This question is from textbook Advanced Mathematics

Found 2 solutions by vleith, jim_thompson5910:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Collecting like terms is the correct first step
%282x%2By%29+%2B+%283-5x%29i+=+1+-7i
%282x+%2B+y+-1%29+%2B+%283%2B7+-5x%29i+=+0
%282x%2B+y+-1%29+%2B+%2810-5x%29i+=+0
For a complex number equal zero, both the real and the imaginary parts must be 0.
So
2x+%2B+y+-1+=+0
10-5x+=+0
-5x+=+-10
x+=+2
Substituting back into the real part
2x+%2B+y+-1+=+0
4+%2B+y+-+1+=+0
y+=+-3

Make sense now?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that %282x%2By%29+%2B+%283-5x%29i+=a%2Bbi. So this means that a=2x%2By and b=3-5x. From the number 1+-7i+, we see that a=1 and b=-7.



b=3-5x Start with the second equation.


-7=3-5x Plug in b=-7.


-10=-5x Subtract 3 from both sides.


2=x Divide both sides by -5.


So the first answer is x=2


a=2x%2By Move onto the first equation


1=2%282%29%2By Plug in a=1 and x=2


1=4%2By Multiply


-3=y Subtract 4 from both sides.



So the first answer is y=-3


So the solutions are x=2 and y=-3