# Thread: Finding real numbers in equations containing complex numbers

1. ## 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?

2. 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.

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