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Math Help - [SOLVED] Complex No.s

  1. #1
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    Exclamation [SOLVED] Complex No.s

    How exactly do I do these questions:

    1. z = 1 + \sqrt{3} . Find the smallest positive integer n for which z^n is real and evaluate z^n for this value of n. Show that there is no integral value of n for which z^n is imaginary.

    2. Find the modulus of \frac{7-i}{3-4i}. Evaluate tan[\arctan\frac{4}{3} - \arctan\frac{1}{7}]. Hence, find the principal argument of \frac{7-i}{3-4i} in terms of \pi.
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  2. #2
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    Oh w8, found the solutions ...

    SORRY!
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  3. #3
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    Quote Originally Posted by xwrathbringerx View Post
    1. z = 1 + \sqrt{3} . Find the smallest positive integer n for which z^n is real and evaluate z^n for this value of n. Show that there is no integral value of n for which z^n is imaginary.
    I am sure that you mean z = 1 + \sqrt 3 \color{red}~i. In that case \arg (z) = \frac{\pi }{3}.
    What is the smallest n such that n\left(\frac{\pi }{3}\right)=k\pi, that is a multiple of \pi.

    Is the any n such that n\left(\frac{\pi }{3}\right)=k\left(\frac{\pi }{2}\right)?
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