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Math Help - Complex Number - Finding the Modulus

  1. #1
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    Complex Number - Finding the Modulus

    Hi

    Can someone tell me what is wrong with my answer to the following question

    Find the modulus: j(1+jcos\theta+sin\theta)

    =j+j^2cos\theta+jsin\theta
    =j-cos\theta+jsin\theta
    =\sqrt{j^2+cos\theta^2+j^2sin\theta^2}
    =\sqrt{-1+cos\theta^2-sin\theta^2}
    =\sqrt{-1+1-sin\theta^2-sin\theta^2}
    =\sqrt{-2sin\theta^2}

    P.S
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  2. #2
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    First, write your complex number in terms of the real and imaginary parts:

    \displaystyle j(1 + j\cos{\theta} + \sin{\theta}) = j + j^2\cos{\theta} + j\sin{\theta}

    \displaystyle = j - \cos{\theta} + j\sin{\theta}

    \displaystyle = -\cos{\theta} + j(1 + \sin{\theta}).


    So the modulus is

    \displaystyle \sqrt{(-\cos{\theta})^2 + (1 + \sin{\theta})^2}

    \displaystyle = \sqrt{\cos^2{\theta} + 1 + 2\sin{\theta} + \sin^2{\theta}}

    \displaystyle = \sqrt{1 + 1 + 2\sin{\theta}}

    \displaystyle = \sqrt{2 + 2\sin{\theta}}

    \displaystyle = \sqrt{2(1 + \sin{\theta})}.
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