Find the argument of the complex number — 3+ 8i in the interval 0°

Question

Find the argument of the complex number — 3+ 8i in the interval 0°<theta<360⁰, rounding to the nearest tenth of a degree if necessary

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Khải Quang 5 months 2021-08-22T07:55:02+00:00 1 Answers 4 views 0

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    2021-08-22T07:56:15+00:00

    Answer:

    The argument is 290.6°

    Step-by-step explanation:

    For a complex number:

    Z = a + b*i

    The argument is:

    θ = Atan(b/a)

    Where Atan(x) is the inverse function of the tangent function, such that:

    Atan(tan(x)) = x

    tan(Atan(x)) = x

    In this case, we have the complex number:

    Z = -3 + 8*i

    The argument of this complex number will be:

    θ = Atan(8/-3) = -69.4°

    But we want 0°< θ <360⁰

    Also, remember that the trigonometric functions have a periodicity of 360°

    Then:

    cos(θ + n*360°) = cos(θ)

    With n integer.

    This means that our angle is equivalent to:

    -69.4° + 360° = 290.6°

    Then the argument is 290.6°, this one is on the desired interval (0°, 360°)

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