Intereting Posts

Geometrical interpretation of a group action of $SU_2$ on $\mathbb S^3$
Proof of the independence of the sample mean and sample variance
existence of closed forms of certain Dirichlet series
How to find the Galois group of a polynomial?
Is every $T_4$ topological space divisible?
Are these two Banach spaces isometrically isomorphic?
Why can't you square both sides of an equation?
Next step to take to reach the contradiction?
Convolution of multiple probability density functions
Coin with unknown bias flipped N times with N heads, what is p(h)?
What is the chances of a duplicate in this equation
Do these $\sigma$-algebras on second countable spaces coincide?
universal property in quotient topology
An Identity for Pell-numbers
Relations (Binary) – Composition

How do you get the roots of the equation in algebraic form?

I have no idea after changing to a trigonometric form.

The angle was not simple.

$z^4- \sqrt3 i+1=0$

- Finding a solution to $\sum _{n=1}^{n=k} \frac{1}{n^x}+\sum _{n=1}^{n=k} \frac{1}{n^y}=0$
- What's $(-1)^{2/3}\; $?
- How to choose a proper contour for a contour integral?
- Non-integer powers of negative numbers
- $z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
- Evaluate the integral using the theory of residues: $\int_{-\infty}^{\infty} \frac{dx}{(x^2+1)^2(x^2+16)}$

- If $i^2=-1$, then what about $(-i)^2=-1$?
- Proving $ z^n + \frac1{z^n} = 2\cos(n\theta) $ for $z = \cos (\theta) + i\sin(\theta)$
- Applications of complex numbers to solve non-complex problems
- Prove that $\{n^2f\left(\frac{1}{n}\right)\}$ is bounded.
- For what values $\alpha$ for complex z $\ln(z^{\alpha}) = \alpha \ln(z)$?
- Do $z^{3/4}=-1 $ solutions exist?
- How to extend this extension of tetration?
- Complex Conjugate of Complex function
- Distinguishing Primitive vs. Nonprimitive Roots of Unity
- Infinity times $i$

**Hint**: We have $$z^4 =\sqrt {3}i-1 =2 (\frac {\sqrt {3}}{2}i-\frac {1}{2}) =2 (\cos 120^\circ +i \sin 120^\circ) $$

Can you take it from here?

- Is there another simpler method to solve this elementary school math problem?
- 2 Questions about Markov chain
- Prove even integer sum using induction
- Proof of $\lim_{n \to \infty} {a_n}^{1/n} = \lim_{n \to \infty}(a_{n+1}/a_n)$
- When is the image of a null set also null?
- Summing $\frac{1}{a}-\frac{1}{a^4}+\frac{1}{a^9}-\cdots$
- Is this equivalent to Cauchy-Schwarz Inequality?
- Fixed points in category theory
- clarification asked for 'difference between convolution and crosscorrelation?'
- Why isn't there a good product formula for antiderivatives?
- Formula for solving for Cx and Cy…
- Is a least squares solution to $Ax=b$ necessarily unique
- Matrix exponential convergence
- Looking for induction problems that are not formula-based
- Why is $i^i$ real?