# Finding real numbers in equations containing complex numbers

• Sep 27th 2010, 01:53 PM
Mbrown141
Finding real numbers in equations containing complex numbers
Ok, teacher gave us a quick exercise overnight, to help with tomorrow's work. Was 2 parts, I've done the first and I'm sure it's right, I just have no clue where to start the second.

A) Find the real numbers p and q where :

p+q+i(p-q) = 4+2i

So, we know i(p-q) has to be the +2i part, and p+q has to be 4 -

p - q = 2 and p + q = 4

p=4-q

4-2q=2

q=1.

P+1=4

p=3

The second one is -

2(p+iq)=q-ip-2(1-i)

Now, I've scribbled out a lot so far. I started by expanding all the brackets, leaving -

2p+2iq=q-ip-2-2i

Which has no like terms at all. So I tried re-arranging to get p on it's own -

2p=q-ip-2-2i-2iq

p=$\displaystyle \frac{q-ip-2-2i-2iq}{2}$

But that just makes me even more confused. Anyone know if I'm on the right path?
• Sep 27th 2010, 03:14 PM
Zamzen
You should think in terms of real part and imaginary part.
so simplify it to p(2+i) + q(2i-1) = -2+2i
real part is equal to -2
so Re (-2 + 2i) = -2 = 2p -q
and Im (-2 + 2i) = 2 = p + 2q.
from there u should be able to solve it by breaking out for example p in both equations and solve for q and then for p.
u will get that q is 1.2 and p is -0.4.