List of top Mathematics Questions on Algebra asked in KEAM

Given that $i^{2}=-1$. If $z_{1}=(7+i\sqrt{5})^{2}+(7-i\sqrt{5})^{2}$ and $z_{2}=(3+2i)^{3}-(3-2i)^{3}$, then

If $z_{1}=1+3i$, $z_{2}=-3i+5$, then $(z_{1}\overline{z_{2}}+z_{2}\overline{z_{1}})+(z_{1}\overline{z_{2}}+z_{2}\overline{z_{1}})$ is equal to

$\left|\frac{\cos\alpha+i\sin\alpha}{\sin\alpha-i\cos\alpha}\right|^{1000}+\left|\frac{\sin\alpha+i\cos\alpha}{\cos\alpha-i\sin\alpha}\right|^{2000}$ is equal to

Let $f(x)=\frac{2025x+2026}{2027x-2025},x\in\mathbb{R},x\ne\frac{2025}{2027}$ be a function. Then $f^{1000}(100)$, where $f^{2}(x)=f(f(x))$ is equal to

Let $f(x)=x^{2}+2x+3,x\le-1$. Then the domain of the inverse of $f(x)$ is

Given that $i^{2}=-1$. Then $(i^{1})(i^{2})(i^{3})\dots(i^{2026})$ is equal to

Solve the equation: \[ \frac{(3x - 4)^2}{9} - \frac{(4x - 3)^2}{8} = 1 \quad \text{(length of the latus rectum)} \]