the voltage v of an ac circuit can be found using the formula v = iz, where i is current and z is impedance…

the voltage v of an ac circuit can be found using the formula v = iz, where i is current and z is impedance. if i = 2 - 3i amps and z = 7 + 5i ohms, determine the voltage. simplify your answer as much as possible.\n\nv = \\boxed{} volts

the voltage v of an ac circuit can be found using the formula v = iz, where i is current and z is impedance. if i = 2 - 3i amps and z = 7 + 5i ohms, determine the voltage. simplify your answer as much as possible.\n\nv = \\boxed{} volts

Answer

Explanation:

Step1: Recall the formula for voltage

We know that ( V = IZ ), where ( I = 2 - 3i ) and ( Z = 7 + 5i ). So we need to multiply these two complex numbers.

Step2: Multiply the complex numbers

Using the distributive property (FOIL method) for complex numbers: ((a + bi)(c + di)=ac + adi + bci + bdi^2), and since ( i^2=- 1). [ \begin{align*} V&=(2 - 3i)(7 + 5i)\ &=2\times7+2\times5i-3i\times7-3i\times5i\ &=14 + 10i-21i-15i^2\ &=14-11i-15\times(- 1)\ &=14-11i + 15\ &=(14 + 15)-11i\ &=29-11i \end{align*} ]

Answer:

(29 - 11i)