Find a polynomial equation with integer coefficients that has the given numbers as solutions and the indicated degree
1 - i, 7i; degree 4
Stacey Warren - Expert brainly.com
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What exactly do you need help with? Try replacing x for the given roots 1 - i and 7i in the equations and see which one is a true equality
yeah, I've tried that. I don't know what to do
post your work and maybe I can help you find where you did mistakes
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I don't even have an idea how to do it
Since you have roots \(1-i\) and \(7i\), you must also have roots \(1+i\) and \(-7i\). This is an important property of the complex numbers you should probably remember for your class.
Now we have 4 different roots, so we can just find what \[(x-(1-i))(x-(1+i))(x-7i)(x+7i)\]is equal to, and you should have a degree 4 polynomial with integer coefficients.
The specific property says that if you have a root \(a+bi\), you must also have a root \(a-bi\) if your polynomial is in the real numbers.