Algebra 2 question

Question

If (x + y) + (2i) = 4 + (x - y)i then (x , y) =

Answer 1

(x+y)+2i=4+(x-y)i

x+y=4 (real part)

x-y=2 (imaginary part)

add

2x=6

x=3

3+y=4 so y=1

(x,y)=(3,1)

Answer 2

Since the real and complex solutions are independent ( you can think of them as independent vectors) ,

you must set the real components and the imaginary components equal separately and solve:

Solve : (x + y) + ( 2 i ) = 4 + (x - y)i

This leads to a system of equations:

(x+y) = 4 ; for the real components

2 = ( x-y) ; for the imaginary components

Arranging again so that x & y are on the same side, we have:

x + y = 4

x - y = 2

This is a 2 X 2 system . Solving for x,

2 x = 6 => x = 3. Substituting , we get y =1 . Plug back in;

( 3+1) +2 i = 4 + (3-1)i

( 4) + 2 i = 4 + (2) i ; is an identity so we have verified the solution.

Answer 3

Hello Hriday,

Based on how these equations are written, we can conclude that x + y = 4 and x - y = 2

After solving for x and y, we get that (x,y) is (3,1)