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calculus

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find the modulus and the argument of the following complex numbers:
15-4i and a-ai where a is greater than 0

  • calculus - ,

    if z = a + b i
    r^2 = sqrt( a^2 + b^2)
    and a = r cos T
    and b = r sin T

    so
    if a = 15
    and b = -4
    then r^2 = 15^2 + (-4)^2 = 225+16
    r = 15.524
    cos T = 15/15.524
    so T = 14.9 or -14.9
    sin T = -4/15.52
    so T = -14.9 or (180-14.9)=165.1
    T = -14.9 which is +345.1 in the fourth quadrant satisfies both, so that is it. (Besides we could see that 15-4i was in quadrant 4)

    r = sqrt (2 a^2) = a sqrt 2
    fourth quadrant again
    so
    sin T = -1/sqrt (2) = = -.707
    T = -45 degrees which is + 315 degrees

  • calculus - ,

    im sorry they were two different questions you have to find the modulus and the argument
    ex.15-4i
    modulus-4
    but i don't know what the argument is

  • calculus - ,

    I did them as two different questions
    for #1
    modulus = r = 15.524
    argument = T (for theta) = -14.9 degrees (or +345.1 degrees)

    for #2
    modulus = a sqrt 2
    theta = argument = -45 (or 315) degrees

  • calculus - ,

    thanks

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