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

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In summary, to find the complex and real part of z, we can use the equation 4z-z(3+i)=-i+3i and factor out z to get z(4-(3+i))=-i+3i. We then use the complex conjugate to solve for z and get the final answer of z=-2+i.
  • #1
aisha
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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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  • #2
Nevermind, sorry for confusing you.
 
Last edited:
  • #3
Im not sure how to do that?
 
  • #4
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)
 
  • #5
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
 

What is the complex part of z?

The complex part of z is the imaginary component of a complex number, denoted by the letter "i". It is the coefficient of the imaginary unit in the form a + bi, where a is the real part and bi is the complex part.

What is the real part of z?

The real part of z is the real component of a complex number, denoted by the letter "a". It is the coefficient of the real number in the form a + bi, where a is the real part and bi is the complex part.

How do you find the complex part of z?

The complex part of z can be found by taking the coefficient of the imaginary unit "i" in the form a + bi. This is represented by the number "b".

How do you find the real part of z?

The real part of z can be found by taking the coefficient of the real number in the form a + bi. This is represented by the number "a".

Why is it important to understand the complex and real parts of z?

Understanding the complex and real parts of z is important in many fields, such as mathematics, physics, and engineering. It allows for the representation and manipulation of complex numbers, which are essential in solving various problems and equations. Additionally, understanding these components helps in visualizing and understanding the behavior of complex numbers in the complex plane.

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