If `z=cos30^@+isin30^@`, find `z^7`

Explanation

To solve the problem where \( z = \cos 30^\circ + i \sin 30^\circ \) and we need to find \( z^7 \), we will use De Moivre's theorem. Here’s a step-by-step solution:

### Step 1: Identify the values
We have:
- \( \theta = 30^\circ \)
- \( r = 1 \) (since \( \cos 30^\circ \) and \( \sin 30^\circ \) are both values of a unit circle)

### Step 2: Apply De Moivre's Theorem
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