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What is the conjugate of the complex numbers two minus seven π?
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We begin by recalling what we actually mean by the complex number π§.
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This is 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 π§ whereas π, the coefficient of π, is its imaginary part.
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We then define the complex conjugate of π§ to be equal to π§ star.
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And we find this by changing the sign of the imaginary part.
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And so, for a complex number π plus ππ, its conjugate is π minus ππ.
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Letβs look at our complex number then.
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Well, itβs two minus seven π.
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The real part of π§ is two.
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And its imaginary part is negative seven.
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We said that, to find the conjugate of a complex number, we change the sign of the imaginary part.
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So the complex conjugate of π§, π§ star, will have an imaginary part of positive seven.
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Its real part remains as two.
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So we find π§ star is equal to two plus seven π.
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And so, we found the conjugate of the complex number two minus seven π.
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Itβs two plus seven π.