https://file.aiquickdraw.com/mathbot/file/1726541548278ddc3tmpe.jpg

The expression in the image is:

\[
(1 + i)^{3200} - (1 - i)^{3200}
\]

Let's simplify this.

### Step 1: Express \((1 + i)\) and \((1 - i)\) in polar form
\[
1 + i = \sqrt{2} \text{cis}\left(\frac{\pi}{4}\right)
\]
\[
1 - i = \sqrt{2} \text{cis}\left(-\frac{\pi}{4}\right)
\]
where \(\text{cis}(\theta)\) stands for \(\cos(\theta) + i\sin(\theta)\).

### Step 2: Use De Moivre’s Theorem
By De Moivre’s Theorem

Learn how to simplify the complex number expression (1 + i)^3200 - (1 - i)^3200 using polar form and De Moivre's Theorem. This problem is suitable for advanced high school or college-level students studying complex numbers and exponents.

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