Question 583804
Instead of calculating (1/2-(1/2)i)^4, I'm going to calculate 4*(1/2-(1/2)i)^4 


4*(1/2-(1/2)i)^4


(sqrt(2))^4*(1/2-(1/2)i)^4


(sqrt(2)*(1/2-(1/2)i))^4


(sqrt(2)/2-(sqrt(2)/2)i))^4


(cos(pi/4)-i*sin(pi/4))^4


cos(4*pi/4)-i*sin(4*pi/4)


cos(pi)-i*sin(pi)


-1-i*(0)


-1



So 4*(1/2-(1/2)i)^4 = -1. 


But we really want to know the value of (1/2-(1/2)i)^4


So all we need to do is divide both sides by 4 to get 


(1/2-(1/2)i)^4 = -1/4



So the final answer is <a href="http://www.codecogs.com/eqnedit.php?latex=\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}" target="_blank"><img src="http://latex.codecogs.com/gif.latex?\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}" title="\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}" /></a>