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For two given complex numbers a and b, is it true that |a-b| = |a|-|b| ?

Posted by White Group Mathematics on April 24, 2015 at 12:40 PM



For two given complex numbers a and b, is it true that  |a-b| = |a|-|b| ?




Student X









Generally, it isn't true. However, in specific instances, |a-b|  can be equal to  |a|-|b|.  This happens when arg(a)= arg(b). Bearing in mind |a-b| always represents geometrically the physical distance between the two complex numbers a and b, here is a visual representation for this unique case:









Another instance worth noting is when arg(b)= arg(a) - π, then |a-b| actually becomes |a|+|b|:




Hope the above clarifies. Peace.





Best Regards,


Mr Koh

Categories: Math Queries

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