How can I show $i^{-1} = -i$, where $i$ is the imaginary unit? Here's what I've tried: $i^{-1} = (-1)^{-1/2} = \dots ?$

How to compute a linear fractional transformation that maps a circle to a given circle? For example, let $C_1$ be the circle $|z+(2+i)|=1$ and $C_2$ be th...

OK I know this sounds pretty stupid, but I am stuck on solving $x^{{2}/{3}}=4$. I rewrote it to $\sqrt[3]{x^2}=4$, but I don't know what to do next. ...

How can one show that the product of two banded matrices is a banded matrix with upper and lower bandwidths equal to the sum of the upper and lower bandwi...

I'm talking about the short version of the area of a pentagram inscribed in a circle when the radius is given and so Area $=1.123r^2$. I only got thi...

$ABC$ is an isosceles triangle inscribed in a circle with centre $O$.Suppose the top vertex is $A$, the right vertex is $B$ and the left vertex is $C$. Al...

I have this problem from my Graphics course. Given this transformation matrix: $$\begin{pmatrix} -2 &-1& 2\\ -2 &1& -1\\ 0 &0& 1\\...

I'm trying to find if it is possible to find the lengths of the base and height of a right triangle with only the hypotenuse and the area (or the per...

This is the question: Solve $$x^2 \frac{\text{d}y}{\text{d}x} = y^2 - 3xy -5x^2 .$$ Are there any straight line solutions? If so, state them. For the case...

I need to find a formula for the nth partial sum of the series: $ 2 + \frac 23 + \frac 29 + \frac {2}{27} + .... + \frac {2}{3^{n-1}} + ... $ then I need ...