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Is negative nine the complex conjugate of the number negative nine?
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Letβs begin by recalling what we actually mean by the complex conjugate of a number.
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Let π be a complex number of the form π plus ππ, where π and π are real constants.
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We say that π is the real part of our complex number, whereas the imaginary part is π.
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Itβs the coefficient of π.
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We define π star, which we sometimes also call π bar, as the complex conjugate of the number π.
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Itβs π minus ππ.
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And we find the complex conjugate by changing the sign of the imaginary part.
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So letβs write our number negative nine as a complex number.
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Negative nine itself is a real number.
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So if weβre going to write it as a complex number, weβre going to write it as negative nine plus zero π.
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Its real part is negative nine, and its imaginary part is zero.
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We said that the complex conjugate is found by changing the sign of the imaginary part.
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So the complex conjugate of our complex number is negative nine minus zero π.
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But of course, thatβs simply negative nine.
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And so negative nine is indeed the complex conjugate of the number negative nine.