Question

use the formula ( v = i cdot r ), where ( i ) represents the current and ( r ) represents the resistance

1. find ( r ) if ( v = 2 - i ) and ( i = 7 + 4i )

(use ( r=\frac{v}{i} ))
type a response

Explanation:

Step1: Substitute the given values into the formula

Given \(V = 2 - i\) and \(I = 7 + 4i\), and the formula \(R=\frac{V}{I}\), we substitute to get \(R=\frac{2 - i}{7 + 4i}\).

Step2: Rationalize the denominator

Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of \(7 + 4i\) is \(7-4i\).

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Since \(i^{2}=-1\), we have:

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Step3: Simplify the fraction

Divide each term in the numerator by the denominator:
\(R=\frac{10}{65}-\frac{15i}{65}=\frac{2}{13}-\frac{3}{13}i\)

Answer:

\(\frac{2}{13}-\frac{3}{13}i\)