
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 27th, 2017, 04:24 AM  #1 
Member Joined: Dec 2015 From: England Posts: 30 Thanks: 0  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

February 27th, 2017, 05:04 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,009 Thanks: 1042 
$z^2 + 2z  i \sqrt{3} = 0$ 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 $z = 1 + \sqrt{\dfrac 3 2 }+\dfrac{i}{\sqrt{2}}$ $z = 1  \sqrt{\dfrac 3 2 }\dfrac{i}{\sqrt{2}}$ 

Tags 
form, puting, putting 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Putting in to general terms?  cj2007  Abstract Algebra  3  August 14th, 2015 08:01 AM 
Putting stakes on different odds  ricsi046  Applied Math  1  January 3rd, 2015 12:47 AM 
Help understanding/putting together this type of problem  WWRtelescoping  Algebra  13  March 6th, 2014 06:30 AM 