
complex numbers
Hello, would really appreciate if anyone could answer this questions for me ... i'm really stuck! If possible, could you show all working out because otherwise i will get lost!
* Find all the fifth roots of  1.
* Find all the third roots of 2 + 2 i .
*3. If w = (z  i)/(z+i) and z lies below the real axis, show that w lies outside the unit circle
 w  = 1.
How will w move as z travels along the real axis from  infinity to + infinity ?
*4. Prove that the area A ( a, b, c ) of the triangle in the complex plane with corners at a, b, c
must be C (Complex), ordered in anticlockwise fashion, is given by the formula:
A ( a, b, c ) = (i/4)( ab`  a`b + b c ` b`c + c a`  c`a )
Thank you !

You can't get ANY of these?
1 and 2 require ONLY DeMoivre. Convert the values to polar coordinates and you should see it.
The third looks like an algebra problem. It could be a little messy, I guess.
Let's see if you can get through those while I think about #4, or someone else chimes in.

the first two questions were dealt with here. i like Soroban's method the most

Note that $\displaystyle (1)^{1/5} = 1$. If you let $\displaystyle \zeta = \cos \frac{2\pi}{5}+i\sin \frac{2\pi }{5}$. Then the roots are $\displaystyle 1,\zeta,\zeta^2.\zeta^3.\zeta^4$.