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

Question 583804: how do you expand this complex number in a standard complex number format?
(1/2-1/2i)^4
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (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(24713) (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

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