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Thread: Complex Numbers!

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    Complex Numbers!

    Hey, I got two questions;

    I'll attach the images as I cannot use LaTeX for some reason.

    1. https://imgur.com/a/CFbQErW (I tried expanding and simplifying using bionomial, I do get correct answers but of course they are not in the forms of cot and so on, I get straight square roots, expected).

    2. https://imgur.com/a/eF2Su32 (The only real place I am struggling is the last part, deducing the cos(2O) statement, rest is completed).

    Thank You!

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    Re: Complex Numbers!

    Q5

    Last edited by Drongoski; 26 Jul 2018 at 3:50 PM.
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    Re: Complex Numbers!

    Thank you buddy, that was very nicely explained!
    Except, how was the second last line derived? I understood up till 1+cosO+isinO/1-cosO-isinO...the half angles one, I am slightly lost
    Last edited by harshsyd; 26 Jul 2018 at 4:12 PM.

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    Re: Complex Numbers!





    I think the start of that second last line you were talking about should read:

    HSC 2018: English Adv. [80] • Maths Ext. 1 [98] • Maths Ext. 2 [95] • Chemistry [87] • Software Design [95]

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    Re: Complex Numbers!

    For your second question:

    Let .



    Note:


    Similarly,


    Going back to the original identity: multiplying the expression on the RHS and taking the real part of both sides,



    And a few more lines of working give the required identity.
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    Re: Complex Numbers!

    Thanks!

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