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Math Help - Finding radius for De Moivre's Theorem

  1. #1
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    Finding radius for De Moivre's Theorem

    My question has (square root 2 / 2 - i square root 2 / 2)^20 and I must express this in the form a+bi.

    I was able to find the angle of 315 degrees. Now I must find the radius, is it 1?

    I've divided everything by square root of 2 since that is what it can simplify to, and then used the answer and used the formula r= square root of a^2+b^2. I got "1". Can you check if this is the radius?
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  2. #2
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    Quote Originally Posted by thekrown View Post
    My question has (square root 2 / 2 - i square root 2 / 2)^20 and I must express this in the form a+bi.

    I was able to find the angle of 315 degrees. Now I must find the radius, is it 1?

    I've divided everything by square root of 2 since that is what it can simplify to, and then used the answer and used the formula r= square root of a^2+b^2. I got "1". Can you check if this is the radius?
    HI

    (\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2}i)^{20}

    =(\frac{\sqrt{2}}{2})^{20}(1-i)^{20}

    =\frac{2^{10}}{2^{20}}(-2^{10})

    =1

    (1-i)^2=-2i

     <br />
(1-i)^{20}=(-2i)^{20}=-2^{10}<br />

    so the magnitude would be 1 .
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