electricity use the formula v = ci, where v is the voltage, c is the current, and i is the impedance. the…

Explanation:

Step1: Rearrange the formula for current

Given $V = CI$, we can solve for $C$ as $C=\frac{V}{I}$. Here, $V = 24 - 8j$ and $I=4 - 2j$. So $C=\frac{24 - 8j}{4 - 2j}$.

Step2: Rationalize the denominator

Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $4 - 2j$ is $4 + 2j$. [ \begin{align*} C&=\frac{(24 - 8j)(4 + 2j)}{(4 - 2j)(4 + 2j)}\ &=\frac{24\times4+24\times2j-8j\times4-8j\times2j}{4^{2}-(2j)^{2}}\ &=\frac{96 + 48j-32j-16j^{2}}{16 - 4j^{2}} \end{align*} ] Since $j^{2}=- 1$, we have: [ \begin{align*} C&=\frac{96 + 48j-32j-16\times(-1)}{16-4\times(-1)}\ &=\frac{96 + 16+48j-32j}{16 + 4}\ &=\frac{112 + 16j}{20}\ &=\frac{112}{20}+\frac{16j}{20}\ &=\frac{28}{5}+\frac{4}{5}j \end{align*} ]

Answer:

$\frac{28}{5}+\frac{4}{5}j$