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Math Help - Write 1-i exponential form

  1. #1
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    Write 1-i exponential form

    I have to write 1-i in exponential form. Please check my answer. If it is okay, yeah! If it is incorrect, could you help me?

    r=sq.rt.(1^2 - (i)^2)

    r=sq.rt.(1 + 1)

    r=sq.rt.(2)

    arctan 1/1 = pi/4 (45 degrees) cos pi/4 = .707, sin pi/4 = .707

    .707/.707 =1

    My answer: sq.rt.2(e^ipi/4)

    Is this correct?
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  2. #2
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    Hello,

    The problem is that it's arctan 1/(-1), because it's 1+(-1)i
    so this gives the angle -pi/4
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  3. #3
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    You have some mistaken ideas.
    \begin{gathered}<br />
  r = \left| {a + bi} \right| = \sqrt {a^2  + b^2 }  \hfill \\<br />
  r = \left| {1 - i} \right| = \left| {1 + ( - 1)i} \right| = \sqrt {1^2  + ( - 1)^2 }  = \sqrt 2  \hfill \\ <br />
\end{gathered} .

    \arg (1 - i) = \arctan \left( {\frac{{ - 1}}{1}} \right) =  - \frac{\pi }{4}.

    So 1 - i = \sqrt 2 e^{\displaystyle\frac{{ - \pi }}{4}i}
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  4. #4
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    Quote Originally Posted by Joanie View Post
    r=sq.rt.(1^2 - (i)^2)

    Is this correct?
    If z = x+iy, then r = \sqrt{x^2 + y^2}, so the above step is conceptually wrong...You should have written r = \sqrt{1^2 + (-1)^2}
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