+0

# complex number

-1
85
1
+255

Solve for $z$ in the following equation: $2-iz = 1 + 3iz$.

Feb 21, 2021

#1
+25658
+2

Solve for $$z$$ in the following equation: $$2-iz = 1 + 3iz$$.

$$\begin{array}{|rcll|} \hline 2-iz &=& 1 + 3iz \\ 2-1-iz-3iz &=& 0 \\ 1-4iz &=& 0 \quad | \quad \times i\\ 1*i-4i^2z &=& 0 \\ i-4i^2z &=& 0 \quad | \quad \mathbf{i^2 = -1} \\ i-4(-1)z &=& 0 \\ i+4z &=& 0 \\ 4z &=& -i \\ \mathbf{z} &=& \mathbf{-\dfrac{i}{4}} \\ \hline \end{array}$$

Feb 21, 2021