Solution
V = IR is called Ohm's Law. It gives the relationship in a circuit between the voltage V (in volts), the current I (in amperes), and the resistance R (in ohms).
Explanation:
Here we have a complex number operation. According to Ohm's law V=I*R, so:
[tex]\begin{gathered} V=38+i \\ I=9-2i \end{gathered}[/tex]
[tex]R=\frac{V}{I}=\frac{38+i}{9-2i}[/tex]
we need to remove the complex number on the denominator, so we have to multiply by its complement on both side
[tex]\begin{gathered} \frac{38+i}{9-2i}*\frac{9+2i}{9+2i} \\ \frac{342+76i+9i+2i^2}{81+18i-18i-4i^2} \\ =\frac{342+85i+2(-1)}{81-4(-1)} \end{gathered}[/tex]
where
[tex]i^2=-1[/tex][tex]\begin{gathered} \frac{342+85i-2}{81+4} \\ \frac{340+85i}{85} \\ \frac{85(4+i)}{85} \\ 4+i \end{gathered}[/tex]
Therefore the answer is
[tex]R=4+i[/tex]
