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 October 17th, 2011, 01:20 AM #1 Senior Member   Joined: Sep 2011 Posts: 140 Thanks: 0 complex number Okay I have a question, well actually I solved it, but I don't know if it's correct. It would be great if you guys could correct my mistakes if any are made, Thank you. So we have two complex numbers, $z_1= (1+\sqrt{3})^{m}$and $z_2=(1-i)^{n}$ the modulus of $z_1$ is $2^{m}$ and the modulus of $z_2= 2^{\frac{n}{2}}$ the argument of $z_1= \frac{m\pi}{3}$ and the argument of$z_2= \frac{-n\pi}{4}$ hence find the smallest positive integer m,n for $z_1=z_2$ since 0 is an integer, the smallest m and n is 0.
 October 17th, 2011, 02:50 AM #2 Global Moderator   Joined: Dec 2006 Posts: 18,686 Thanks: 1522 Zero isn't a positive integer. You seem to have "i" missing from the definition of $z_{\small1}.$
 October 17th, 2011, 02:57 AM #3 Senior Member   Joined: Sep 2011 Posts: 140 Thanks: 0 Re: complex number but argument and modulus is correct right?
 October 17th, 2011, 03:14 PM #4 Global Moderator   Joined: Dec 2006 Posts: 18,686 Thanks: 1522 Without knowing the correct version of the problem, it's impossible to tell.
 October 18th, 2011, 05:09 AM #5 Senior Member   Joined: Sep 2011 Posts: 140 Thanks: 0 Re: complex number Yea, I made a typo, there is an i in the $z_1$. So having that said, is the mod and arg correct? Also, what would be m and n?
 October 18th, 2011, 05:38 AM #6 Global Moderator   Joined: Dec 2006 Posts: 18,686 Thanks: 1522 Where is the i in the $z_{\small1}$?
 October 18th, 2011, 05:45 AM #7 Senior Member   Joined: Sep 2011 Posts: 140 Thanks: 0 Re: complex number square root 3
 October 18th, 2011, 06:37 AM #8 Global Moderator   Joined: Dec 2006 Posts: 18,686 Thanks: 1522 Re: complex number You found the modulus of each number correctly. For equality, m = n/2. The arguments were nearly right. If the complex numbers are equal, m needs to be a multiple of 3. What else is needed?

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