Melody

What would you like to sketch?

sin 90degrees = 1 

I know this becasue sin(angle) is given by the y value on the unit circle.

You make a log by cutting down a tree.   

Unless it is an icecream log. Then you would need a freezer and and some cream. 

Thanks guest that makes sense.

I'll just write my version of what you have said in LaTex.

\(\begin{align} \sqrt{-i}&=\sqrt{\frac{1-2i+1}{2}}\\ &=\sqrt{\frac{1-2i-i^2}{2}}\\ &=\sqrt{\frac{(1-i)^2}{2}}\\ &=\frac{\sqrt{(1-i)^2}}{\sqrt 2}\\ &=\frac{1-i}{\sqrt 2}\\ &=\frac{\sqrt 2(1-i)}{2}\\ &=\frac{\sqrt 2}{2}-\frac{\sqrt 2\;i}{2}\\ \end{align}\)

Ok that is good although it is only one of the 2 answers

With the aid of a quick sketch I can see that the 2 roots are

\(\sqrt{-i}=\pm \left[\frac{\sqrt{ 2}}{2} (1-i)\right]\)       

I still cannot see the error in my #2 answer though    

Here it is :)

A Spooky Halloween to you too Asad :)

Find the polynomial function in standard form with leading coefficient 2 that has the given degree and zeroes.

Polynomial with degree 3, with -2, 1/2, and 4/3 as zeroes.

f(x)=2(x+2)(x-0.5)(x-4/3)

Now just expand it out.

Try watching and learning from this clip:

6 people

there is no head of the tabel so the first person is just a place marker so there are really only 5 people whose positions matter.

But John and sam are tied together so thet are the equaivalent of one person.

so that is only 4 people.

4!     *2   because it could be john, sam or sam, john. 

2*3*4*2 = 48 permutations.