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 Complex Analysis Complex Analysis Math Forum

February 27th, 2017, 04:24 AM   #1
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Joined: Dec 2015
From: England

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putting in form z=x+iy

Please could some one help with how to put this equation into the form x+iy=z as I am stuck
Attached Images Capture.jpg (9.2 KB, 12 views) February 27th, 2017, 05:04 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,530 Thanks: 1390 $z^2 + 2z - i \sqrt{3} = 0$ complete the square $(z+1)^2 - 1 - i\sqrt{3} = 0$ $(z+1)^2 = 1+i\sqrt{3}$ $z+1 = \pm \sqrt{1+i\sqrt{3}}$ $z = -1 \pm \sqrt{1+i\sqrt{3}}$ Now we need to deal with the radical. $1+i\sqrt{3} = 2e^{i\pi/3}$ $\sqrt{1+i\sqrt{3}} = \sqrt{2}e^{i\pi/6} = \sqrt{\dfrac 3 2 }+\dfrac{i}{\sqrt{2}}$ so $z = -1 + \sqrt{\dfrac 3 2 }+\dfrac{i}{\sqrt{2}}$ $z = -1 - \sqrt{\dfrac 3 2 }-\dfrac{i}{\sqrt{2}}$ Thanks from Andrzejku98 Tags form, puting, putting Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post cj2007 Abstract Algebra 3 August 14th, 2015 08:01 AM ricsi046 Applied Math 1 January 3rd, 2015 12:47 AM WWRtelescoping Algebra 13 March 6th, 2014 06:30 AM

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