How Do You Isolate and Solve for z in the Equation 4z - z(3+i) = -1+3i?

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To isolate and solve for z in the equation 4z - z(3+i) = -1 + 3i, the first step is to factor out z, resulting in z(4 - (3+i)) = -1 + 3i. This simplifies to z(1 - i) = -1 + 3i. The next step involves using the complex conjugate to solve for z. After applying the necessary steps, the solution is found to be z = -2 + i. The discussion highlights the importance of factoring in solving complex equations.
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Find the complex and real part of z:
4z-z(3+i)=-1+3i

I think I am solving for z but I am having problems isolating it. Can some1 help please.
 
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Nevermind, sorry for confusing you.
 
Last edited:
Im not sure how to do that?
 
4z-z(3+i)=-1+3i

Factor out the z: z(4-(3+i) = -i + 3i ---> z(1-i) = -i + 3i

Hope you can figure out the next step (hint: it may involve the complex conjugate)
 
Thanks!

vincebs said:
4z-z(3+i)=-1+3i

Factor out the z: z(4-(3+i) = -i + 3i ---> z(1-i) = -i + 3i

Hope you can figure out the next step (hint: it may involve the complex conjugate)

THANKS SOOOO MUCH Vincebs I got the answer thank you, I couldn't get the answer because I never thought of factoring thanks sooo much. :smile:

The correct answer to this problem is z=-2+i
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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