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thank you so much for taking the time.

 

Describe all solutions to z -3w - 2iw + 4iz = - 8 + 12i where z  and  w are complex numbers.

 

 

 

THANK YOU SO MUCH FOR HELPING ME!!!

 Mar 29, 2023
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We can begin by rearranging the given equation:

z - 3w - 2iw + 4iz = -8 + 12i

Simplifying the left side by grouping the real and imaginary terms of z and w separately:

z + 4iz - 3w - 2iw = -8 + 12i

Factor out z and w:

z(1+4i) - w(3+2i) = -8 + 12i

Now we can solve for one variable in terms of the other. Let's solve for z in terms of w:

z = (-8+12i+w(3+2i))/(1+4i)

To find all solutions for z and w, we need to substitute any possible values for w and solve for z.

Alternatively, we could solve for w in terms of z:

w = (-8+12i+z(1+4i))/(3+2i)

Again, we can substitute any possible values for z and solve for w.

Therefore, there are infinite solutions to this equation since we can choose any complex number for z or w, and the other variable can be calculated using the equation above.

 Mar 29, 2023

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