Melody

For all complex numbers z,

let f(z) = z^2 if z is not real, f(z) = 2z if z is real.

Find f(f(f(f(1+i))))

\(f(i+1)=(1+i)^2=2i\\ f(2i)=(2i)^2=-4\\ f(-4)=2*-4=-8\\ f(-8)=2*-8=-16\)

It is the same as the diagonal of a circle on its right side.

Use Pythagoras's theorem to find the length of AC

A   'thanks you '  would have been nice.

Thanks from me Al..foil      

\(1.\overline{234}= 1\frac{234}{999}=1\frac{26}{111}=\frac{111+26}{111}=\frac{137}{111}\)

Just like you already said  

1+1+3+9+8+5 = 27

there are 27 scores

the middle score will be (27+1)/2 = 14th

The 14th score is 78

So the median score is 78

There are 4 scores of 86,   This is the score that occurs most often.  So  Mode=86

The mean is the hardest one to get.  You have to add up all the scores

41+52+67+68+ .....etc.... =

then divide the the answer by 27

You are very welcome :)

I don't think that you have copied this question in full Jenny.

Thanks guest, but you have a couple of little errors

when you multiply or divide by a negative number you have to turn the sign around

so

-x        < -7

-x*-1  >  -7*-1

x > 7

So the smallest integer that works is 8    (because 8 is bigger than 7.)

I followed what you did so far Tiggsy  BUT I still don't know how to finish it.

Maybe I have brain freeze.   

\(f(x) = 1 - \int_0^x [f(t)]^2 \ dt\\ \)

\(\displaystyle \frac{d}{dx}f(x)= - [f(x)]^{2}\\ \int\displaystyle \frac{d}{dx}f(x)dx= -\int [f(x)]^{2}dx\\ f(x)= -\displaystyle \int [f(x)]^{2}dx\\ \)

???