Mathegoras

Complex numbers › Roots of unity and complex roots › Counting complex solutions

Unit complex numbers with a Re-Im condition

High school · ●●●○○ 50 pts

How many complex numbers zz satisfy the following two conditions: ∣z∣=1|z|=1 and Re⁡(z100)=Im⁡(z200)\operatorname{Re}\left(z^{100}\right)=\operatorname{Im}\left(z^{200}\right)?

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