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Math Help - Need Help, complex

  1. #1
    Member Rimas's Avatar
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    Need Help, complex

    If a =2 +i then in the form of a+bi what does a^-1 equal
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    Quote Originally Posted by Rimas View Post
    If a =2 +i then in the form of a+bi what does a^-1 equal
    It means the multiplicative inverse,

    \frac{1}{2+i}\cdot \frac{2-i}{2-i}=\frac{2-i}{4+1}=\frac{2}{5}-i\frac{1}{5}
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    Member Rimas's Avatar
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    What?
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    Quote Originally Posted by Rimas View Post
    What?
    I multiplied by the "conjugate" to clear the denominator from imaginary numbers. Note, I multiplied both the numerator and denominator.

    The meaning of a^{-1} is definied as the inverse, meaning,
    \frac{1}{2+i}
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    This is one of my favorite questions.
    The multiplicative inverse of a complex number z is:
    z^{ - 1}  = \frac{{\overline z }}{{\left| z \right|^2 }}.

    Of course z\not = 0+0i
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