Simplify \(Z\times 1\) to \(Z\).
\[\begin{aligned}&Z=3\imath +4\\&Z\times 2=1-\imath \end{aligned}\]
Regroup terms.
\[\begin{aligned}&Z=3\imath +4\\&2Z=1-\imath \end{aligned}\]
Regroup terms.
\[\begin{aligned}&Z=4+3\imath \\&2Z=1-\imath \end{aligned}\]
Break down the problem into these 2 equations.
\[Z=4+3\imath \]
\[Z=2Z\]
Solve the 1st equation: \(Z=4+3\imath \).
Already solved. No work needed.
\[Z=4+3\imath \]
\[Z=4+3\imath \]
Solve the 2nd equation: \(Z=2Z\).
Subtract \(Z\) from both sides.
\[0=2Z-Z\]
Simplify \(2Z-Z\) to \(Z\).
\[0=Z\]
Switch sides.
\[Z=0\]
\[Z=0\]
Collect all solutions.
\[Z=4+3\imath ,0\]
Z=4+3*IM,0
