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Math Help - Imaginary to trig notation

  1. #1
    Junior Member Greymalkin's Avatar
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    Imaginary to trig notation

    Convert (1-i)(2+2i) to trig notation and then multiply

    I get:

    {\sqrt{2}{(cos315+isin315)}*{\sqrt{8}{(cos45+isin4  5)}}
    4{(cos360+isin360)}
    4

    Book answer is: 4({cos42+isin42)

    My first part is wrong, why???

    Also I have a general question other than this current problem. Why are the angles always the same in each point?
    Last edited by Greymalkin; July 20th 2012 at 08:17 AM.
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  2. #2
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    Re: Imaginary to trig notation

    You're nearly right. The answer is 4i.
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  3. #3
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    Re: Imaginary to trig notation

    Quote Originally Posted by Greymalkin View Post
    Convert (1+i)(2+2i) to trig notation and then multiply

    I get:

    {\sqrt{2}{(cos45+isin45)}*{\sqrt{8}{(cos45+isin45)  }}
    4{(cos90+isin90)}
    4

    Book answer is: 4({cos42+isin42)
    You textbook is mistaken.
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  4. #4
    Junior Member Greymalkin's Avatar
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    Re: Imaginary to trig notation

    Quote Originally Posted by a tutor View Post
    You're nearly right. The answer is 4i.
    It appears I was overhasty in posting this because I've mixed up the answers from the text, the actual answer says 4, why would you say it is 4i? isnt i*0=0?
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  5. #5
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    Re: Imaginary to trig notation

    Quote Originally Posted by Greymalkin View Post
    It appears I was overhasty in posting this because I've mixed up the answers from the text, the actual answer says 4, why would you say it is 4i? isnt i*0=0?
    Because before you edited it the answer was 4i.
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  6. #6
    Junior Member Greymalkin's Avatar
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    Re: Imaginary to trig notation

    It also appears that my brain isnt into math on fridays
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  7. #7
    Super Member ILikeSerena's Avatar
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    Re: Imaginary to trig notation

    Hmm, I do not know what you edited, but the answer should be 4i.

    You seem to have deduced an angle of 315 degrees for (1+i).
    But that angle should be 45 degrees.

    It seems you had that before, but then you also got 4, which is still wrong - it really should be 4i.
    Note that \sin 90 = 1.
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  8. #8
    Junior Member Greymalkin's Avatar
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    Re: Imaginary to trig notation

    Quote Originally Posted by ILikeSerena View Post
    Hmm, I do not know what you edited, but the answer should be 4i.

    You seem to have deduced an angle of 315 degrees for (1+i).
    But that angle should be 45 degrees.

    It seems you had that before, but then you also got 4, which is still wrong - it really should be 4i.
    Note that \sin 90 = 1.
    Sorry, the real question is (1-i)(2+2i). Although my question was answered my editing was not finished, apologies.
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