SOLUTION: how do you expand this complex number in a standard complex number format? (1/2-1/2i)^4

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: how do you expand this complex number in a standard complex number format? (1/2-1/2i)^4      Log On

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 Question 583804: how do you expand this complex number in a standard complex number format? (1/2-1/2i)^4Found 2 solutions by jim_thompson5910, solver91311:Answer by jim_thompson5910(28595)   (Show Source): You can put this solution on YOUR website!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 $\left(\frac{1}{2}-\frac{1}{2}i \right )^4 = -\frac{1}{4}$ Answer by solver91311(16897)   (Show Source): You can put this solution on YOUR website! Use FOIL to square the binomial just like any other binomial. Remember that . Then square the result. John My calculator said it, I believe it, that settles it