In polar coordinates, what is the impedance of a network comprising a 400-ohm-reactance inductor in parallel with a 300-ohm resistor?

To find the impedance of a network consisting of a 400-ohm-reactance inductor in parallel with a 300-ohm resistor, we start by understanding the behavior of these components in an AC circuit.

The inductor has a reactance of 400 ohms. This means its impedance can be represented in polar coordinates as j400 ohms (where "j" represents the imaginary unit used in electrical engineering). The parallel combination of a resistor and an inductor requires the calculation of their combined impedance.

The resistor is simply 300 ohms, which can be written as 300 ohms + j0 ohms.

In polar coordinates, the impedance of components in parallel can be calculated using the following formula for two components:

Z_total = (Z1 * Z2) / (Z1 + Z2)

Here, Z1 is the impedance of the inductor (j400 ohms) and Z2 is the impedance of the resistor (300 ohms).

When we perform the calculation:

1. Convert the impedances to their rectangular forms: Z1 = 0 + j400 and Z2 = 300 + j0.

2. Use the formula to find the total impedance.

The resulting impedance will be in the