If `z = x - iy` and `z'^(1/3) = p +iq,` then `1/(p^2+q^2)(x/p+y/q)` is equal to

Options

A. `-2`
B. `-1`
C. 2
D. 1

Explanation

To solve the problem step by step, we start with the given information and work through the algebra carefully.

### Step 1: Define the variables
Given \( z = x - iy \) and \( z^{1/3} = p + iq \).

### Step 2: Express \( z \) in terms of \( p \) and \( q \)
We can express \( z \) as:
\[
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