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 December 15th, 2012, 07:31 AM #1 Newbie   Joined: Dec 2012 Posts: 28 Thanks: 0 Help complex numbers Need help about this: Express the following in the form $a+bi$: $\frac{1-3i}{1+i}-\frac{i}{2+i}$
 December 15th, 2012, 07:59 AM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Help complex numbers Try multiplying both terms by 1 in the form of the conjugate of the denominator over itself. Then add the resulting real and imaginary components. What do you get?
 December 15th, 2012, 08:11 AM #3 Newbie   Joined: Dec 2012 Posts: 28 Thanks: 0 Re: Help complex numbers I get this: 4-4/3i , but I'm not sure that it is right:/
 December 15th, 2012, 08:26 AM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Help complex numbers No, that's not correct. Can you post your work so we can see where you are making an error?
 December 15th, 2012, 08:51 AM #5 Newbie   Joined: Dec 2012 Posts: 28 Thanks: 0 Re: Help complex numbers No, it says it have very large size ( can you post your?
 December 15th, 2012, 09:20 AM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Help complex numbers Type it out (should only take a minute or two at the most). I would much rather see typed work than images of handwritten work anyway.
 December 15th, 2012, 09:09 PM #7 Newbie   Joined: Dec 2012 Posts: 28 Thanks: 0 Re: Help complex numbers 1-3i/1+i - i/2+i= (1-3i)(-2-i)+(-i)(1+i) / (1+i)(-2-i) = (-5+5i)+(-i+1) / -1-3i = -5+5i-i+1 / -1-3i = -4+4i / -1-3i = 4 - 4/3 i Re= 4, Im= -4/3i
 December 15th, 2012, 09:15 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Help complex numbers I suggest simplifying: $\frac{1-3i}{1+i}\cdot\frac{1-i}{1-i}-\frac{i}{2+i}\cdot\frac{2-i}{2-i}$
 December 15th, 2012, 10:52 PM #9 Newbie   Joined: Dec 2012 Posts: 28 Thanks: 0 Re: Help complex numbers I get this after simplyfing: -2-4i/2 - 2i+1/5
 December 15th, 2012, 11:05 PM #10 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Help complex numbers If you mean (-2-4i)/2 - (2i+1)/5 then that is correct. This can further be simplified to: $-1-2i-\frac{2}{5}i-\frac{1}{5}$ Now you need collect together the real and imaginary parts.

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