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Why does multiplying a fraction by its conjugate not change its value?

April 26, 2017conjugate fraction Mathematics multiplying value

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Why does multiplying a fraction by its conjugate not change its value?

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You are NOT multiplying the “fraction by its conjugate”. You are multiplying BOTH the top and the bottom of the fraction by the same complex number. That is equivalent to multiplying the fraction by 1, which does not change its value. For example, if you want to simplify (3+2i) / (4+3i) you would multiply both top and bottom by (4-3i). This is the same as multiplying the fraction by (4-3i) / (4-3i) = 1. The reason this simplifies the fraction is that when you multiply a complex number by its conjugate the imaginary parts cancel out leaving you with a real number. So, you end up with a real number on the bottom of the fraction, which you can distribute to the two parts of the top.