Questions: Find the resistance in a circuit where the voltage is 4+2i volts and the current is -4i amperes. The resistance R in an electrical circuit is given by the formula R=V/I, where V is the voltage, measured in volts, and I is the current in amperes. The resistance in the circuit is R= ohms. (Type your answer in the form a+bi. Use integers or fractions for any numbers in the expression.)

I'll solve this electrical circuit problem step by step.

Find the resistance in a circuit where the voltage is $4+2i$ volts and the current is $-4i$ amperes.

Identify the given values

We are given:

• Voltage $V = 4+2i$ volts
• Current $I = -4i$ amperes
• The resistance formula: $R = \frac{V}{I}$

Calculate the resistance using the formula

$R = \frac{V}{I} = \frac{4+2i}{-4i}$

To divide complex numbers, I'll multiply both numerator and denominator by the complex conjugate of the denominator: $R = \frac{4+2i}{-4i} \cdot \frac{4i}{4i} = \frac{(4+2i)(4i)}{(-4i)(4i)} = \frac{(4+2i)(4i)}{-16i^2}$

Since $i^2 = -1$, we have: $R = \frac{(4+2i)(4i)}{-16(-1)} = \frac{(4+2i)(4i)}{16}$

Expand the numerator

$R = \frac{(4)(4i) + (2i)(4i)}{16} = \frac{16i + 8i^2}{16} = \frac{16i + 8(-1)}{16} = \frac{16i - 8}{16}$

Simplify the final expression

$R = \frac{16i - 8}{16} = \frac{-8}{16} + \frac{16i}{16} = -\frac{1}{2} + i$

Therefore, the resistance is $R = -\frac{1}{2} + i$ ohms.

\(\boxed{R = -\frac{1}{2} + i}\)

\(\boxed{R = -\frac{1}{2} + i \text{ ohms}}\)