1. Complex number help??

Find "x" and "Y" if

1) 2(x+yi) = x-yi

2) (X+2i)(1-i) = 5+yi

2. Originally Posted by jumko
Find "x" and "Y" if

1) 2(x+yi) = x-yi

Mr F says: Expand and equate the real and imaginary parts on each side:

2x + 2yi = x - yi. Therefore

Equate real parts: 2x = x .... (1)

Equate imaginary parts: 2y = -y .... (2)

Therefore x = y = 0.

2) (X+2i)(1-i) = 5+yi

Mr F says: Use the same approach as above.

..

3. Originally Posted by jumko
1) 2(x+yi) = x-yi
$2x + 2yi = x - yi$

$(2x - x) + (2y + y)i = 0$

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

4. thanks.

But, if it wouldn't be any trouble could you show the process of another slightly more harder one?

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

5. Originally Posted by jumko
thanks.

But, if it wouldn't be any trouble could you show the process of another slightly more harder one?

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

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.