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Saima posted an Question
September 10, 2021 • 16:23 pm 20 points
  • CSIR NET
  • Physical Sciences

Contour integration (why only take e^ipi/4 & e^3ipi/4

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    Bidyut sinha Best Answer

    ok l am telling you...see upper half of complex plane means(+-) x coordinate and (+)iy coordinate...So whatever value of Z u r getting,that should give value in the +- x coordinate and +iy coordinate... Not -iy ...so now ,see for exp(iπ/4) and exp(i3π/4) value gives (cosπ/4+isinπ/4) and (cos3π/4+isin3π/4)...so both sinπ/4 and sin3π/4 giving positive value...that is value lies within +iy ...but for 5π/4, calculate the value of 5π/4,that is sin 225°= (-)0.707 lying in the negative iy plane

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    Bidyut sinha

    Because only exp(i π/4) and exp(3πi/4) lies on the upper half of the complex plane...For more please check the attached picture.

    cropped925613386.jpg
    eduncle-logo-app

    how only both these terms lie on upper half...why cant 5ipi/4 ..i have a doubt in this point

    eduncle-logo-app

    ok l am telling you...see upper half of complex plane means(+-) x coordinate and (+)iy coordinate...So whatever value of Z u r getting,that should give value in the +- x coordinate and +iy coordinate... Not -iy ...so now ,see for exp(iπ/4) and exp(i3π/4) value gives (cosπ/4+isinπ/4) and (cos3π/4+isin3π/4)...so both sinπ/4 and sin3π/4 giving positive value...that is value lies within +iy ...but for 5π/4, calculate the value of 5π/4,that is sin 225°= (-)0.707 lying in the negative iy plane

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