My Math Forum Complex number problem

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 January 20th, 2013, 05:24 PM #1 Newbie   Joined: Jan 2013 Posts: 13 Thanks: 0 Complex number problem z^2/4 - (3?2 + i3) = 0 put the roots on argend diagram, I have an idea how to do this but am not confident, any help would be appreciated.
 January 20th, 2013, 06:31 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond Re: Complex number problem I assume you want to find z in the form a + bi; a, b ? ?. $\frac{z^2}{4}\,-\,3\sqrt{2}\,-\,3i\,=\,0$ $z^2\,=\,12\sqrt{2}\,+\,12i$ $(a\,+\,bi)^2\,=\,a^2\,+\,2abi\,-\,b^2$ $a^2\,-\,b^2\,=\,12\sqrt{2}$ $2ab\,=\,12$ $a\,=\,\pm\sqrt{6\sqrt{2}\,+\,6\sqrt{3}}$ $b\,=\,\frac{6}{a}$
 January 21st, 2013, 02:48 AM #3 Global Moderator   Joined: Dec 2006 Posts: 19,295 Thanks: 1686 $b\,=\,\frac{\small6}{a}\,=\,\pm\sqrt{6\sqrt3\,-\,6\sqrt2}$

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### complex numbers and argend

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