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Math Help - De Moivre's Theorem finding powers

  1. #1
    Junior Member Cyberman86's Avatar
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    Question De Moivre's Theorem finding powers

    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.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by Cyberman86 View Post
    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

    225\cdot 7 =1575=4\cdot 360+135

    so this tell us that 1575^\circ and 135^\circ are coterminal angles

    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})
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  3. #3
    MHF Contributor

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    Are you missing this?
    7\left( {225^ \circ  } \right) = 1575^ \circ   \approx 135^ \circ
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