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Omni-MATH / Let z be a complex number. In the complex plane, the distance from z to 1 is 2 , and the distance from z² to 1 is 6 . What is the real part of z ?

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problem

Let zz be a complex number. In the complex plane, the distance from zz to 1 is 2 , and the distance from z2z^{2} to 1 is 6 . What is the real part of zz ?
Plain-text mathematical notation (without MathML)
Let z be a complex number. In the complex plane, the distance from z to 1 is 2 , and the distance from z² to 1 is 6 . What is the real part of z ?
Original LaTeX notation
Let $z$ be a complex number. In the complex plane, the distance from $z$ to 1 is 2 , and the distance from $z^{2}$ to 1 is 6 . What is the real part of $z$ ?

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