Given:
Z= sqrt. of 2(cos(225degrees) +i sin(225degrees))^7
This the formula I'm using
Z^n= r^n(cos n deita + i sin n deita)
I tried to follow the formula but i keep getting it wrong.
The formula is correct. Note that
$\displaystyle 225\cdot 7 =1575=4\cdot 360+135$
so this tell us that $\displaystyle 1575^\circ$ and $\displaystyle 135^\circ $ are coterminal angles
$\displaystyle z^7=2^7\left( \cos(135^\circ)+i\sin(135^\circ)\right)=2^7\left( -\frac{\sqrt{2}}{2}+i\frac{\sqrt{2}}{2}\right)=2^6(-\sqrt{2}+i\sqrt{2})$