Perform the Indicated Operation $Z$ Can Be Calculated Using the Equation $$\frac { 1 } { Z } = \left( \frac { 1 } { Z _ { 1 } } + \frac { 1 } { Z _ { 2 } } \right)$$

Multiple Choice

Perform the indicated operation. Give answers in rectangular form expressing real and imaginary parts to four decimal
places.
-In a parallel electrical circuit, the impedance $Z$ can be calculated using the equation
$$\frac { 1 } { Z } = \left( \frac { 1 } { Z _ { 1 } } + \frac { 1 } { Z _ { 2 } } \right)$$
where $Z _ { 1 }$ and $Z _ { 2 }$ are the impedances for the branches of the circuit. The phase angle measures the phase difference between the voltage and the current in an electrical circuit. If the impedance $\mathrm { Z }$ is expressed in the form $\mathrm { a } + \mathrm { bi }$ , $\theta$ can be determined by the equation $\tan \theta = \mathrm { b } / \mathrm { a }$ . Determine the phase angle $\theta$ (in degrees) for a parallel circuit in which $Z _ { 1 } = 10 + 20 \mathrm { i }$ and $Z _ { 2 } = 30 + 10 \mathrm { i }$ .

A) $60 ^ { \circ }$
B) $30 ^ { \circ }$
C) $0 ^ { \circ }$
D) $45 ^ { \circ }$