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calculus

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Write the complex number -4 x 3^1/3 - 4i in exponential form.

I'm not sure how I use euler's formula to solve for this. A brief explanation would be greatly appreciated.

  • calculus - ,

    Does the "x" indicate multiplication, or is it an unknown? Does the 4 multi-ply (3^1/3) - 4i or just 3^(1/3) ?

    Find the magnitude of the complex number first. Call it C. Then write your number as
    C*e^(i*z)
    using Euler's formula.
    e^iz = cos z + i sin z

    The magnitude of
    -4 *(3^1/3 - 4i)
    is
    4*sqrt[3^(2/3) + 16] = 17.01
    so you can write
    -4 *(3^1/3 - 4i)
    = 17.01*(-0.3392 +0.9406 i)
    Now find the number z (in radians) for which
    cos z = -0.3392 and sinz = 0.9406

    It will be in the second quadrant
    z = 1.9169

    The answer would be 17.01 exp(1.9169i),

    but it depends upon whether I interpreted what you wrote correctly. You need to use parenthese and explain the "x"

  • calculus - ,

    Sorry for the misunderstanding. The X is a multiplication sign and the 4 is multiplied to the cubed root of 3.

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