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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: 7,958 Thanks: 1146 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: 2,256 Thanks: 926 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! 

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cartesian, complex, numbers, polar 
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