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Dividing/ factoring x^2 by (-2i+1)x

When looking for a coefficient of x to multiply with (-2i+1)x to give x^2, the answer is given as (-2/5 - 1i/5)x, in expanding out the brackets I can see how this leads to x^2. I couldn`t come to this answer myself as I wasn`t sure about what technique should be used here? If anyone could give me some guidance as to what method is used here in dividing x^2 by a complex polynomial ( (-2+i)x ), that would be great, thanks.
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mqb2766
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Original post by itlstallion69
When looking for a coefficient of x to multiply with (-2i+1)x to give x^2, the answer is given as (-2/5 - 1i/5)x, in expanding out the brackets I can see how this leads to x^2. I couldn`t come to this answer myself as I wasn`t sure about what technique should be used here? If anyone could give me some guidance as to what method is used here in dividing x^2 by a complex polynomial ( (-2+i)x ), that would be great, thanks.


Is the first term (-2+i)x? If so, its just the complex conjugate
(-2 - i)
divided by the magnitude (squared)
2^2 + 1^2 = 5
which is
(-2/5 - i/5)
The complex conjugate gives you a real coefficient and dividing by the magnitude (squared) gives you a unity coefficient.
Original post by itlstallion69
When looking for a coefficient of x to multiply with (-2i 1)x to give x^2, the answer is given as (-2/5 - 1i/5)x, in expanding out the brackets I can see how this leads to x^2. I couldn`t come to this answer myself as I wasn`t sure about what technique should be used here? If anyone could give me some guidance as to what method is used here in dividing x^2 by a complex polynomial ( (-2 i)x ), that would be great, thanks.


if you divide x^2 by (-2i 1)x and then rationalise it you should get the answer. So you would write it as a fraction with x^2 as the numerator and (-2i 1)x as the denominator. Cancel out the x's and then rationalise
(edited 5 years ago)
Thanks, very helpful, got the answer now.

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