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Find the real part, the imaginary part, and the absolute value of sin.pdf

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Find the real part, the imaginary part, and the absolute value of sin (x - iy). Solution sin(x-iy)=sinx.cosiy-cosx.siniy Since siniy=i sinhy ,cosiy=coshy Sin(x-iy)=sinx.coshy- cosx.i sinhy = sinx.1/2 (e^y +e^-y) -cosx.i.1/2(e^x-e^-x) Real part=1/2 sinx(e^y+e^-y) Imaginary part=-1/2 cosx(e^x-e^-x) Absolute value=1/2{sinx(e^y+e^-y)+cosx(e^x-e^-x)}.

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Find the real part, the imaginary part, and the absolute value of sin (x - iy). Solution sin(x-iy)=sinx.cosiy-cosx.siniy Since siniy=i sinhy ,cosiy=coshy Sin(x-iy)=sinx.coshy- cosx.i sinhy = sinx.1/2 (e^y +e^-y) -cosx.i.1/2(e^x-e^-x) Real part=1/2 sinx(e^y+e^-y) Imaginary part=-1/2 cosx(e^x-e^-x) Absolute value=1/2{sinx(e^y+e^-y)+cosx(e^x-e^-x)}

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  • 1. Find the real part, the imaginary part, and the absolute value of sin (x - iy). Solution sin(x-iy)=sinx.cosiy-cosx.siniy Since siniy=i sinhy ,cosiy=coshy Sin(x-iy)=sinx.coshy- cosx.i sinhy = sinx.1/2 (e^y +e^-y) -cosx.i.1/2(e^x-e^-x) Real part=1/2 sinx(e^y+e^-y) Imaginary part=-1/2 cosx(e^x-e^-x) Absolute value=1/2{sinx(e^y+e^-y)+cosx(e^x-e^-x)}