# The Square of A Complex Number

**Algebra**Level 2

\[ \large\displaystyle \alpha = \frac{1}{ \sqrt{2}} + \frac{1}{ \sqrt{2}}i \quad , \quad \alpha^2 = \, ? \]

**Notation**: \(i\) is the imaginary number \(\sqrt{-1}\).

\[ \large\displaystyle \alpha = \frac{1}{ \sqrt{2}} + \frac{1}{ \sqrt{2}}i \quad , \quad \alpha^2 = \, ? \]

**Notation**: \(i\) is the imaginary number \(\sqrt{-1}\).

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