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Math Help - complex numbers

  1. #1
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    complex numbers

    find argument and modulus of z=1+itan(theta)

    Arg z=theta, and modulus(z)= sec (theta)


    case1 0<theta<pi/2

    case 2: pi/2<theta< pi

    case 3: pi<theta<3pi/2

    case 4: 3pi/2<theta<pi


    here x=1 and y =tan theta so either the complex no lies in the first quadrant or the fouth quadrant so case 2 and 3 shld be invalid ,but in text there is an anwer for each case hw is that possible ,pls share ur ideas
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  2. #2
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    Re: complex numbers

    Hey spacemenon.

    You are right that 1 + i*tan(theta) can only be in the fourth quadrant however theta can be in any quadrant.

    Remember that theta can be in 0 to 2*pi even though tan(theta) only has a principle branch of -pi/2 to pi/2.
    Thanks from spacemenon
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  3. #3
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    Re: complex numbers

    But even if that is the case case 2 and case 3 is invalid
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  4. #4
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    Re: complex numbers

    Remember that you are looking at theta and not tan(theta).
    Thanks from spacemenon
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