Question

If (2+i)(x+yi)=1+3i, where x and y are real numbers, write two equations connecting x and y, and solve them.

Answer 1

(2x-3y)+i(2y+x) = 1 + 3i
compare coff ... and solve for x and y

Answer 2

How?

Answer 3

(2+i)(x+yi)=1+3i
2x +xi +2yi + yi^2 =1+3i
(2x -y) +(x +2y)i = 1+3i
So
2x -y =1
x+2y = 3

Answer 4

treat the real part and the imaginary part separately

Answer 5

(2+i)(x+yi) = 1+3i
=>2x-y + i(x+2y) = 1+3i

compare real and imaginary parts.
so, 2x-y=1 and x+2y=3

solve the two linear equations, to get x and y, and enjoy!

Answer 6

Do you understand?

Answer 7

Yes, thank you :)

Answer 8

Welcome :)