# Tagged Questions

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### About the identity $e^{i\pi}=-1$

I have a question about the famous identity of Euler $e^{i\pi}=-1$. I opened the other day this question about the number of roots of a complex number with irrational exponent. Under this light and ...
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### Prove that 1 has n distinct roots of order n

I am trying to show that 1 has n distinct roots of degree n, or in other word that the equations $$z^n=1$$ has n different roots over the complex field. I know that the fundamental theorem of Algebra ...
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### Solve the equation $x^{2n} + 1 = 0.$ Use these solutions to find a factorization of $x^{2n} + 1$ with real coefficients.

I am asked to solve the equation $x^{2n} + 1 = 0,$ and to use these solutions to find a factorization of $x^{2n} + 1$ with real coefficients. I am given the hint that pairing factors arising from ...
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### Find all solutions of $z^5+a^5=0$

The task is as follows: Find all solutions of $z^5+a^5=0$, where $a$ is a positive real number. My initial attempt (which leads nowhere) My guess is that i'll have to find the 5 5th roots of ...
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### Existence of holomorphic function with a sequence of zeros in the unit disc

The question is : Prove that there exists a holomorphic function $f$ on the open unit disc $\{z \in \mathbb{C} : |z| <1\}$ with the properties that $f(0) = 0$ and $f(1-1/n)=1$ for every integer $n$ ...
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### Polynomial With Imaginary Roots

Working on question 1 here http://www.sosmath.com/cyberexam/precalc/EA2002/EA2002.html Find a polynomial with integer coefficients that has the following zeros: ...
### Use $\alpha, \beta, \gamma$ roots of a polynomial to construct another polynomial [duplicate]
Let $\alpha, \beta, \gamma$ be roots $\in \mathbb{C}$ of $x^3-3x+1$. Determinate a monic polynomial, degree $3$, witch roots are $1- \alpha^{-1},1-\beta^{-1},1-\gamma^{-1}$ The catch is that i can't ...