Question

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the formula Solve the problem using this formula. Find E, the voltage of a circuit, if I = (16 + i) amperes and R = (2 + 4i) ohms.

Answer 1

To find the voltage of the circuit, we can use Ohm's Law by multiplying the given current with the given resistance. The result is V = 28 + 66i volts.

Step-by-step explanation:

To find the voltage of the circuit, we can use Ohm's Law which states that V = IR, where V is the voltage, I is the current, and R is the resistance.

In this case, the current is given as I = (16 + i) amperes and the resistance is given as R = (2 + 4i) ohms.

Substituting these values into the Ohm's Law equation, we get V = (16 + i) * (2 + 4i).

By multiplying the binomials, we get V = 32 + 64i + 2i + 4i^2, which simplifies to V = 32 + 66i - 4.

Finally, we can write the result as V = 28 + 66i volts.

Answer 2

E = (28 + 66i) Volts

Step-by-step explanation:

Note that: i = √-1 ; i² = -1

Ohm's law: E = IR

E = (16+ i) (2 + 4i)

Expand the equation.

E = 16x2 + 16x4i + ix2 + ix4i

E = 32 + 64i + 2i + 4i²

E = 32 + 64i + 2i + 4(-1)

E = 32 + 64i + 2i - 4

Collect like terms:

E = 32 -4 + 64i + 2i

E = (28 + 66i) Volts