Impedance in a Parallel Circuit

Impedance in an electronic circuit is measured using complex numbers. Below is a drawing of a parallel circuit with the meaning of the electronic symbols.

Parallel circuit with key words

Using the diagram below, if we use the variable r1 for resistance of resistor 1, the variable r2 for resistance of resistor 2, d1 for the resistance of the inductor, and c1 for the resistance of the capacitor, the equation for the impedance of the parallel circuit is Z = (Z1 · Z2) / (Z1 + Z2) where Z1 = r1 + d·i, Z2 = r2 - c·i, and i=square root of -1.

parallel circuit with variables r1, r2, c1, and d1.

Example

r1 = 10 ohm, r2 = 20 ohm, c1 = 5 ohm, d1 = 10 ohm, so Z1 = 10 + 10·i and Z2 = 20 - 5·i. This means that Z = ((10 + 10i)(20 - 5i))/((10 + 10i) + (20 - 5i)).
Using FOIL, (10 + 10i)(20 - 5i) = 200 - 50i + 200i - 50i2 = 200 + 150i - 50·(-1) = 250 + 150i.
(10 + 10i) + (20 - 5i) = (10 + 20) + (10 - 5)i = 30 + 5i.
(250 + 150i) / (30 + 5i) = ((250 + 150i)·(30 - 5i))/((30 + 5i)·(30 - 5i)).
(250 + 150i)·(30 - 5i) = 7500 - 1250i + 4500i - 650i2 = 8150 + 3250i.
(30 + 5i)·(30 - 5i) = 900 - 150i + 150i - 25i2 = 925.
(8150 + 3250i) / 925 = 326/37 + 130/37i.

Problem

A Parallel circuit has a r1 = 7, r2 = 14, d1 = 5, c1 = 7. What is the impedance of the circuit?