Question 1

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 ismeasured in volts, resistance in ohms, and current in amperes.) Find the resistance to electrical flow in a circuitthat has a voltage V = (40+30i) volts and current I = (-5+ 3i) amps._+_i/_Note: Answer in the forma + bi/c. If b is negative make sure to put a negative sign in the answer box.

Complex numbers may be applied to electrical circuits. Electrical engineers use the-example-1

Complex numbers may be applied to electrical circuits. Electrical engineers use the-example-2

Complex numbers may be applied to electrical circuits. Electrical engineers use the-example-3

Question 2

we have the formula

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

substitute given values

Remember that

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator

the conjugate of the denominator is (-5-3i)

so

$\begin{gathered} R=(40+30\imaginaryI)/(-5+3\imaginaryI)*(-5-3i)/(-5-3i)=(-40(5)-40(3i)-30i(5)-30i(3i))/(25-9i^2)=(-200-120i-150i-90i^2)/(25-9(-1))=(-110-270i)/(34) \\ \\ R=(-110-270\imaginaryI)/(34) \\ simplify \\ R=(-55-135\imaginaryI)/(17) \end{gathered}$

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