Read More  www.beeman.us  Important Notice 
This page illustrates a modification to synthetic division to allow division of polynomials with complex coefficients by complex binomials. In order to do this, the simple multiplication operation must be changed to a "FOIL" (First Outer Inner Last) of the now complex coefficients. It should be remembered that the L term is the product of two imaginary factors, and therefore the sign must be switched to account for the fact that i^{2} = 1. As a reminder of this the box containing this factor is tinted red, which perhaps suggests "negative" (at least if you are an accountant).
Complex Synthetic Division Calculator  
Click on the divisor or equation coefficients in the top line to change. Click the "Calculate" button to do synthetic division. 


The default example above is the Complex Synthetic division of
x^{2} + 2x + 2 divided by
(x + 1 + i), which is one of the two conjugate roots.
The result is:
(x + 1  i), which is the other conjugate root.
Divisor  X^{2}  X^{1}  X^{0}  
Real  Imag  Real  Imag  Real  Imag  Real  Imag 
:  :  F  O  F  O  
:  :  L  I  L  I  
Real  Imag  Real  Imag  Real  Imag  
X^{1}  X^{0}  Remainder 
Divisor  X^{2}  X^{1}  X^{0}  
Real  Imag  Real  Imag  Real  Imag  Real  Imag 
1  1  1  0  2  0  2  0 
:  :  1  0  1  1  
:  :  0  1  1  1  
1  0  1  1  0  0  
X^{1}  X^{0}  Remainder 
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