
Trigonometry Trigonometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 17th, 2016, 10:20 AM  #1 
Newbie Joined: Feb 2016 From: uk Posts: 8 Thanks: 3  cartesian and polar complex numbers help please
hi guys, i have a few questions and was wondering if you could help me out and explain the processes involved: the power of J: the expression (2+j5) . . . . . . . . . (3+j)(4j) can be expressed in a single number form (a + jb) as 0.335  j0.241 but i would like to know the process of how you get to that answer. also i would like to know how to turn that equation into polar form any input would be much appreciated. thanks in advance 
February 17th, 2016, 12:58 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,923 Thanks: 1123 Math Focus: Elementary mathematics and beyond 
$\displaystyle \begin{align*}\dfrac{2+5j}{(3+j)(4+j)}&=\dfrac{2+5j}{11+7j}\cdot\dfrac{117j}{117j} \\ &=\dfrac{(2+5j)(117j)}{170} \\ &=\dfrac{57+41j}{170}\end{align*}$ 
February 17th, 2016, 02:24 PM  #3 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,092 Thanks: 852 Math Focus: Wibbly wobbly timeywimey stuff. 
Given $\displaystyle z = a + ib$: Let $\displaystyle a + ib = re^{i \theta} = r~cos( \theta ) + ir~sin( \theta )$ Note that since $\displaystyle a = r~cos( \theta )$ and $\displaystyle b = r~sin( \theta )$ we know that $\displaystyle a^2 + b^2 = r^2$ and $\displaystyle tan( \theta ) = \frac{b}{a}$. So what does this give you for your problem? Dan 
February 18th, 2016, 05:23 AM  #4  
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902  Quote:
You could also do this "one step at a time", rationalizing the denominator: $\displaystyle \frac{2+ 5j}{(3+ j)(4 j)}\frac{3 j}{3 j}= \frac{11+ 13j}{(10)(4j)}$ and then $\displaystyle \frac{11 13j}{10(4 j)}\frac{4+ j}{4+ j}= \frac{57 41j}{10(17)}= \frac{57 41j}{170}$  
February 24th, 2016, 03:49 PM  #5 
Newbie Joined: Feb 2016 From: uk Posts: 8 Thanks: 3 
Thanks for the reply guys, gregs post was pretty useful, I did manage to get to the bottom of it all in the end. Much appreciated! 

Tags 
cartesian, complex, numbers, polar 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Complex numbers: Polar to Cartesian Form  chocolate  Algebra  1  December 11th, 2012 06:03 AM 
Complex number, Polar to Cartesian form  chocolate  Algebra  10  November 21st, 2012 10:16 AM 
Polar to Cartesian #2  ChloeG  Calculus  1  March 6th, 2011 01:15 PM 
complex numberspolar form  jakeward123  Complex Analysis  5  February 9th, 2011 08:15 AM 
Complex numbers to polar form  blackobisk  Algebra  1  April 16th, 2009 05:39 PM 