Find "x" and "Y" if
1) 2(x+yi) = x-yi
2) (X+2i)(1-i) = 5+yi
Thanks, please also do the process of getting the answer not just the answer.
$\displaystyle 2x + 2yi = x - yi$
$\displaystyle (2x - x) + (2y + y)i = 0$
For this to be true for arbitrary x and y then we must have that the real part is exactly 0 and the imaginary part is exactly 0.
So
2x - x = 0
and
2y + y = 0
The solution here is trivial, but the method shown here is the way to do all of these.
-Dan
Well, how about you do a few things for me - I'll help you where required:
1. Expand the left hand side:
(x + yi)(2 + i) = ...........
2. After expanding the left hand side, state:
(a) the real part of the left hand side.
(b) the imaginary part of the left hand side.
3. Set up the following equations:
real part of left hand side = 2x .... (1)
imaginary part of left hand side = -(y + 1) = -y - 1 .... (2)
4. Solve equations (1) and (2) above simultaneously for x and y.