I have the following question and cannot seem to overcome how to contend with equations using $z$ and $\bar z$ together. For example, the below problem:
Find the value of $z \in \Bbb C$ that verifies the equation:
$$3z+i\bar z=4+i$$
For other operations that didn't include mixing $z$ and $\bar z$, I was able to manage by "isolating" $z$ on one side of the equation and finding the real and imaginary parts of the complex numbers (sorry if I'm not using the right terms, it's my first linear algebra course)
I tried with wolfram and it didn't really help.
PS: I'm new to this forum but if it's like other math forums where they send you to hell if you ask for "help with your homework", this "homework" I'm doing is on my own since my semester is over and I just wanted to explore other subjects in the book that weren't covered in class.
Best Answer
Another approach is to take the complex conjugate of your equation: $$3\overline z-iz=4-i.$$ You now have two equations for $z$ and $\overline z$. Now eliminate $\overline z$ from them and solve for $z$.