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Let's work through this problem step by step:

We are given:
\[
\frac{V_A}{Z_1} + \frac{V_A}{Z_2} + \frac{V_A}{Z_3} = I
\]
Where:
- \( Z_1 = 5 \)
- \( Z_2 = 6j \)
- \( Z_3 = -2j \)
- \( I = 1 + j8 \)

We need to solve for \( V_A \) and find its phase in radians.

### Step 1: Factor \( V_A \) out of the equation
\[
V_A \left( \frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3} \right) = I
\]
So:
\[
V_A = \frac{I}{\frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3}}
\]

### Step 2: Calculate the sum of the inverses of the impedances
\[
\frac{1}{Z_1} = \frac{1}{5}
\]
\[
\frac{1}{Z_2} = \frac{1}{6j} = -\frac{j}{6}
\]
\[
\frac{1}{Z_3} = \frac{1}{-2j} = \frac{j}{2}
\]

Now, let's compute the sum:
\[
\frac{1}{Z_1} + \frac{1}{Z_2} + \frac{1}{Z_3}
\]

### Step 3: Calculate \( V_A \) by dividing \( I \) by this result.The value of \( V_A \) is approximately \( 18.97 + j8.38 \). 

The phase of \( V_A \) in radians is approximately \( 0.416 \) radians.

Would you like to see more details or have any specific questions? Here are five related questions to deepen understanding:

1. How can we calculate the magnitude of \( V_A \)?
2. Why do we convert impedances to their reciprocal form when solving this type of equation?
3. How would the solution change if the current \( I \) were different?
4. What is the significance of the phase in an AC circuit?
5. Can we convert the phase from radians to degrees, and how?

**Tip**: Remember that phase angles are critical in AC circuit analysis as they represent the time shift between voltage and current.

Discover how to calculate the phase angle of V_A in radians in a complex impedance circuit involving series impedances of real and imaginary values. This advanced problem is essential for electrical engineering students, involving complex numbers, impedance calculations, and AC circuit analysis.

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