Question

=Complex numbers may be applied to electrical circuits. Electrical engineers use the fact that resistance R toelectrical flow of the electrical current I and the voltage V are related by the formula V RI. (Voltage is measured in volts, resistance in ohms, and current in amperes.) Find the resistance to electrical flow in a circuit(90+20i) volts and current I = (- 5+3i) amps._+_/_Note: Answer in the forma + bi/c. If b is negative make sure to put a negative sign in the answer box.

Answer 1

Since the given formula is

`V=RI`

Since we need to find R, then divide both sides by I

`\begin{gathered} (V)/(I)=(RI)/(I) \\ \\ (V)/(I)=R \\ \\ R=(V)/(I) \end{gathered}`

Since V = (90 + 20i)

Since I = (-5 + 3i), then

`R=((90+20i))/((-5+3i))`

Multiply up and down by the conjugate of (-5 + 3i) which is (-5 - 3i)

`R=((90+20i))/((-5+3i))*((-5-3i))/((-5-3i))`

Simplify up and down

`R=((90)(-5)+(90)(-3i)+(20i)(-5)+(20i)(-3i))/((-5)(-5)-(3i)(3i))`
`R=(-450-270i-100i-60i^2)/(25-9i^2)`

Replace i^2 by -1 and add the like terms

`\begin{gathered} R=(-450-370i-60(-1))/(25-9(-1)) \\ \\ R=(-450-370i+60)/(25+9) \\ \\ R=(-390-370i)/(34) \end{gathered}`

The answer is

`R=([-390]+[-370]i)/(34)`
`R=([-195]+[-185]i)/(17)`