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Math Help - Complex numbers

  1. #1
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    Exclamation Complex numbers

    I am stuck and need help:

    Let z= -1 - sqrt (3i) and u= e^(i3pi/4)

    Write z in exponential form, and u in Cartesian form

    Find the complex roots of z; write answer in Cartesian form

    Find u^1001; in Cartesian form
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  2. #2
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    Quote Originally Posted by LightEight View Post
    I am stuck and need help:

    Let z= -1 - sqrt (3i) and u= e^(i3pi/4)

    Write z in exponential form, and u in Cartesian form

    Find the complex roots of z; write answer in Cartesian form

    Find u^1001; in Cartesian form
    Exponential form for a complex number z=a+ib \Longrightarrow z=|z|e^{i\phi}, where \phi is the argument of z, which can be calculated by Arg(z)=Arctan\,\frac{y}{x} , TAKING INTO ACCOUNT the signs of x, y.

    For example, Arg(-1-\sqrt{3}i)=Arctan\,\sqrt{3}=\frac{\pi}{3}\,\,or\,\  ,\frac{4\pi}{3} . As both the real and the imaginary part of z are negative it is the second option.

    For u^{1001} use exponent rules and the fact that e^h=e^{h+2k\pi i}\,,\,\,k\in \mathbb{Z}

    The rest is simple standard stuff that needs to be studied, understood and practiced in any decent alebra book.

    Tonio
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