Questions on Algebra: Complex Numbers answered by real tutors!

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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
(2x+y) + (3-5x)i = 1 -7i solve for x & y <BR> I lumped the i's and the numbers together then squared everything to get <BR> 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
: (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
(2x+y) + (3-5x)i = 1 -7i solve for x & y <BR> I lumped the i's and the numbers together then squared everything to get <BR> 29x^2+4xy-104x+y^2-2y=-101
The answer is x=2 & y=-3, but I can't get there.
Answer by vleith(1174) About Me  (Show Source):
You can put this solution on YOUR website!
Collecting like terms is the correct first step
(2x+y) + (3-5x)i = 1 -7i
(2x + y -1) + (3+7 -5x)i = 0
(2x+ y -1) + (10-5x)i = 0
For a complex number equal zero, both the real and the imaginary parts must be 0.
So
2x + y -1 = 0
10-5x = 0
-5x = -10
x = 2
Substituting back into the real part
2x + y -1 = 0
4 + y - 1 = 0
y = -3

Make sense now?
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
(2x+y) + (3-5x)i = 1 -7i solve for x & y <BR> I lumped the i's and the numbers together then squared everything to get <BR> 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
: (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
(2x+y) + (3-5x)i = 1 -7i solve for x & y <BR> I lumped the i's and the numbers together then squared everything to get <BR> 29x^2+4xy-104x+y^2-2y=-101
The answer is x=2 & y=-3, but I can't get there.
Answer by jim_thompson5910(9390) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that (2x+y) + (3-5x)i =a+bi. So this means that a=2x+y 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+y Move onto the first equation


1=2(2)+y Plug in a=1 and x=2


1=4+y Multiply


-3=y Subtract 4 from both sides.



So the first answer is y=-3


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