
Complex Analysis Complex Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 17th, 2016, 12:06 PM  #1 
Newbie Joined: Jun 2012 Posts: 11 Thanks: 0  write complex number in a+bi form with a and b real
$\frac{z}{(z+1)^2}$, with $z=\frac{1}{2}\sqrt{2}+\frac{1}{2}\sqrt{2}i$ I know the answer is $1\frac{\sqrt{2}}{2}$, but I don't know how to get there. Anybody know which steps I should take? Last edited by skipjack; October 31st, 2016 at 09:30 PM. 
September 17th, 2016, 01:21 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,640 Thanks: 959 Math Focus: Elementary mathematics and beyond 
$\displaystyle \begin{align*}\frac{z}{(z+1)^2}&=\frac{e^{i\pi/4}}{(e^{i\pi/4}+1)^2} \\ &=\frac{e^{i\pi/4}}{e^{i\pi/2}+2e^{i\pi/4}+1} \\ &=\frac12\frac{\sqrt2+\sqrt2i}{i+\sqrt2+\sqrt2i +1} \\ &=\frac{\sqrt2}{2}\frac{1+i}{(\sqrt2+1)(1+i)} \\ &=\frac{\sqrt2}{2}\frac{1}{\sqrt2+1} \\ &=\frac{\sqrt2}{2}(\sqrt21) \\ &=\frac{2\sqrt2}{2} \\ &=1\frac{\sqrt2}{2}\end{align*}$ 
October 31st, 2016, 09:51 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,145 Thanks: 1418 
$\displaystyle \begin{align*}\frac{z}{(z+1)^2}&=\frac{1}{z + 2 + 1/z} \\ &= \frac{1}{2 + \sqrt2} \\ &= \frac{2  \sqrt2}{2} \\ &= 1  \frac{\sqrt2}{2}\end{align*}$ 

Tags 
complex, form, number, real, write 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
How do you write the real number symbol?  123qwerty  Elementary Math  11  August 31st, 2015 03:35 AM 
Exponential form of Complex Number  Naz  Geometry  4  July 24th, 2015 02:55 PM 
complex number to exponential form  marsmallow  Complex Analysis  3  April 21st, 2011 04:12 PM 
Finding real number in complex number  TsAmE  Complex Analysis  1  October 18th, 2010 05:38 PM 
Complex number and polar form  BlackOps  Algebra  2  June 22nd, 2008 05:01 PM 