If (2 - 4i) is a solution to a polynomial equation, is the complex conjugate, 2 + 4i, also a solution?

1 Answer
Jim H
Dec 8, 2015

If the polynomial has Real number coefficients, then the complex conjugate of an imaginary root is also a root.

Explanation:

So, if the coefficients are real numbers, then the answer is "yes.

If the coefficients are not known to be real, then the answer is "maybe yes, maybe no".
#x-(2-4i)=0# has only one zero, namely #2-4i#

#(x-(2-4i))(x-i)=0# has two solutions, #2-4i# and #i#.

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