I’m studying complex analysis. I was reading a section about roots of complex numbers, and I found that $\sqrt{i}$ has two values. ($i$ : imaginary unit) ...

The given equation is $$y^{(4)}+5y^{''}+4y= \sin(x)+\cos(2x)$$ Using the auxiliary equation to find the roots result with $m_{1,2}=\pm i$ and $m...

The remainders of dividing the polynomial $P(x)$ with $x-1$, $x-2$, $x+1$ is $2$, $3$, and $6$ respectively. What is the remainder of dividing the polynom...

After finishing a first calculus course, I know how to integrate by parts, for example, $\int x \ln x dx$, letting $u = \ln x$, $dv = x dx$: $$\int x \ln ...

Bingo cards have $5$ rows and $5$ columns. The column names are B,I,N,G,O. Each column has $15$ possible numbers to choose from $1-15$ for $B$, $16-30$ fo...

I am following Shaferevich's Basic Algebraic Geometry 1.Here quasiprojective variety means open subset of a projective closed set. He defines regular...

I have this matrix below: And i have this question below: Determines whether the row vectors of A are linearly dependent. Explain! Determine the solution ...

I know this question might sound stupid, but hear me out. For a while I took truth values for granted, but recently I've gotten very confused about t...

In order to further along a different proof, I need the following result: Let $G_{1}, G_{2},\cdots , G_{k}$ be groups of orders $n_{1}$, $n_{2}$, $\cdots$...

Hello I have a problem with solving Trigonometric equations. Why this is not true for $0\le\theta\le360$ $$2\sin\theta\cos\theta=\sin\theta$$ $$2\cos\thet...