My Math Forum Lots of imaginary number problems

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 September 15th, 2009, 04:00 PM #2 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 Re: Lots of imaginary number problems Since problem 1 is completely screwed up, I'll address this one only. You have the right idea - multiply numerator and denominator by conjugate of denominator, but you did it completely wrong. You should have (x^2 - y^2 + 2ixy)/(x^2 + y^2)
 September 15th, 2009, 06:53 PM #3 Newbie   Joined: May 2008 Posts: 16 Thanks: 0 Re: Lots of imaginary number problems lol wow i can't believe i didn't square the y's.. alright thanks so I suppose the answer sheet in incorrect?
 September 16th, 2009, 05:59 AM #4 Senior Member   Joined: Mar 2009 Posts: 318 Thanks: 0 2) Is the expression z + (25/z), as posted, or did you mean (z + 25)/z? 3) Let z = a + bi. Then the left-hand side is (3 + a) + (2 + b)i, and the right-hand side is (1 - i)(a + bi) = (2b) + (b - a)i. Equate the real and imaginary parts, and solve the resulting system of equations. 4) You posted the expression [(2/3) + i] + [(3/2) + i], but then referred to "solving". Please clarify. Do you have an expression (as posted) and you need to simplify, or is there more (including an "equals" sign and a variable) and you need to solve? 5) Have you learned about deMoivre's rule yet?
September 16th, 2009, 08:50 PM   #5
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 Originally Posted by stapel 2) Is the expression z + (25/z), as posted, or did you mean (z + 25)/z? 3) Let z = a + bi. Then the left-hand side is (3 + a) + (2 + b)i, and the right-hand side is (1 - i)(a + bi) = (2b) + (b - a)i. Equate the real and imaginary parts, and solve the resulting system of equations. 4) You posted the expression [(2/3) + i] + [(3/2) + i], but then referred to "solving". Please clarify. Do you have an expression (as posted) and you need to simplify, or is there more (including an "equals" sign and a variable) and you need to solve? 5) Have you learned about deMoivre's rule yet?
Alright thanks for your help, I've managed to solve all but 5 which I still don't fully understand, as for the clarification for 2) yes z +(25/z) for 4) I meant my method for simplification and no I havn't yet should but i'll check it out... again thanks for reading all that ^.^

 September 17th, 2009, 03:26 PM #6 Global Moderator   Joined: May 2007 Posts: 6,807 Thanks: 717 Re: Lots of imaginary number problems For 5) x^3+1=(x+1)(x^2 -x +1). I presume you can solve for the roots of x^2 - x +1=0.

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