#### 950**Question:

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• \[ |a + bi| = \sqrt{a^2 + b^2} = 1 \Rightarrow a^2 + b^2 = 1. \]
• \[ a + bi = \cos\left(\frac{\pi}{3}\right) + i\sin\left(\frac{\pi}{3}\right). \]
• \[ \cos\left(\frac{\pi}{3}\right) = \frac{1}{2}, \quad \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}. \]

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