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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: ganges on November 03, 2008, 10:21:54 am

Title: NEED URGENT HELP WITH Complex number conjugates!!!!!
Post by: ganges on November 03, 2008, 10:21:54 am: Umm i still dont understand when and when not to use the conjugate as a factor.
Title: Re: NEED URGENT HELP WITH Complex number conjugates!!!!!
Post by: riadnicolas on November 03, 2008, 10:32:33 am: you only use complex conjugates when all the co-efficients of the function are real numbers
Title: Re: NEED URGENT HELP WITH Complex number conjugates!!!!!
Post by: trinon on November 03, 2008, 12:45:37 pm: So for example I have the equation $P(z) = z^3 + z^2-4z+6$ and I know that $z - 1 + i$ is a factor. Because $P(z)$ only has real coefficients then I can assume that $z - 1 - i$ is also a factor according to the Conjugate Factor Theorem. Multiplying these gives us $(z - 1 + i)(z - 1 - i) = z^2 - 2z + 2$ . To find the third factor (which has to be real), you equate the equations and say $(z^2 - 2z + 2)(z - a) = z^3 - (2 + a)z^2 + 2(1 - a)z - 2a = P(z) = z^3 + z^2-4z+6$ . Now that you have two same looking equations, you equate the coefficients to find that $a = -3$ thus showing the final factor to be $z + 3$ .