Determine the complex number $z$ satisfying the equation $3z+4i\bar{z}=1-8i$.  Note that $\bar{z}$ denotes the conjugate of $z$.
Question:
Determine the complex number $z$ satisfying the equation $3z+4i\bar{z}=1-8i$.  Note that $\bar{z}$ denotes the conjugate of $z$.
Answer:
Let's think step by step.

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-5+4i
Determine the complex number $z$ satisfying the equation $3z+4i\bar{z}=1-8i$.  Note that $\bar{z}$ denotes the conjugate of $z$.
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